Keywords:
heating control
temperature
intermediate moments of time
nonseparated multipoint conditions
complete controllability

The problem of control of rod heating process by changing the temperature along the rod whose ends are thermally insulated is considered. It is assumed that, along with the classical boundary conditions, nonseparated multipoint intermediate conditions are also given. Using the method of separation of variables and methods of the theory of control of finite-dimensional systems with multipoint intermediate conditions, a constructive approach is proposed to build the sought function of temperature control action. A necessary and sufficient condition is obtained, which the function of the distribution of the rod temperature must satisfy, so that under any feasible initial, nonseparated intermediate, and final conditions, the problem is completely controllable. As an application of the proposed approach, control action with given nonseparated conditions on the values of the rod temperature distribution function at the two intermediate moments of time is constructed.

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[1] A.G. Butkovskii: Control Methods for Systems with Distributed Parameters. Nauka, 1975 (in Russian).

[2] A.G Butkovskii, S.A Malyi, and Yu.N. Andreev: Optimal Control of Metal Heating. Moscow, Metallurgy, 1972 (in Russian).

[3] A.I. Egorov: Optimal Control of Thermal and Diffusion Processes. Nauka, 1978 (in Russian).

[4] A.I. Egorov and L.N. Znamenskaya: Introduction to the Theory of Control of Systems with Distributed Parameters. Textbook, Saint Petersburg, LAN, 2017 (in Russian).

[5] E.Ya. Rapoport: Structural Modeling of Objects and Control Systems with Distributed Parameters. Higher School, 2003 (in Russian).

[6] A.N. Tikhonov and A.A. Samarskii: Equations of Mathematical Physics. Nauka, 1977 (in Russian).

[7] V.I. Ukhobotov and I.V. Izmest’ev: A control problem for a rod heating process with unknown temperature at the right end and unknown density of the heat source. Trudy Instituta Matematiki i Mekhaniki, UrO RAN, 25(1), (2019), 297–305 (in Russian), DOI: 10.21538/0134-4889-2019-25-1-297-305.

[8] V.I. Ukhobotov and I.V. Izmest’ev: The problem of controlling the process of heating the rod in the presence of disturbance and uncertainty. IFAC Papers OnLine, 51(32), (2018), 739–742, DOI: 10.1016/j.ifacol.2018.11.458.

[9] V.I. Butyrin and L.A. Fylshtynskyi: Optimal control of the temperature field in the rod when changing the control zone programmatically. Applied Mechanics, 12(84), (1976), 115–118 (in Russian).

[10] M.M. Kopets: Optimal control over the process of heating of a thin core. Reports of the National Academy of Sciences of Ukraine, 7, (2014), 48–52 (in Ukrainian), http://dspace.nbuv.gov.ua/handle/123456789/87951.

[11] N.V.Gybkina, D.Yu. Podusov, and M.V. Sidorov: The optimal control of a homogeneous rod final temperature state. Radioelectronics and Informatics, 2 (2014), 9–15 (in Russian).

[12] E.Y. Vedernikova and A.A. Kornev: To the problem of rod heating. Moscow Univ. Math. Bull., 69, (2014), 237–241, DOI: 10.3103/S0027132214060023.

[13] J.F. Bonnans and P. Jaisson: Optimal control of a parabolic equation with time-dependent state constraints. SIAM Journal on Control and Optimization, 48(7), (2010), 4550–4571.

[14] A. Lapin and E. Laitinen: Iterative solution of mesh constrained optimal control problems with two-level mesh approximations of parabolic state equation. Journal of Applied Mathematics and Physics, 6, (2018), 58–68, DOI: 10.4236/jamp.2018.61007.

[15] K. Kunisch and L. Wang: Time optimal control of the heat equation with pointwise control constraints. ESAIM: Control, Optimisation and Calculus of Variations, 19(2), (2013), 460–485, http://eudml.org/doc/272753.

[16] J.M. Lemos, L. Marreiro, and B. Costa: Supervised multiple model adaptive control of a heating fan. Archives of Control Sciences, 18(1), (2008), 5–16.

[17] S.H. Jilavyan, E.R. Grigoryan, and A.Zh. Khurshudyan: Heating control of a finite rod with a mobile source. Archives of Control Sciences, 31(2), (2021), 417–430, DOI: 10.24425/acs.2021.137425.

[18] V.R. Barseghyan: Control problem of string vibrations with inseparable multipoint conditions at intermediate points in time. Mechanics of Solids, 54(8), (2019), 1216–1226. DOI: 10.3103/S0025654419080120.

[19] V.R. Barseghyan: Optimal control of string vibrations with nonseparate state function conditions at given intermediate instants. Automation and Remote Control, 81(2), (2020), 226–235, DOI: 10.1134/S0005117920020034.

[20] V.R. Barseghyan: Control of Compound Dynamic Systems and of Systems with Multipoint Intermediate Conditions. Nauka, 2016 (in Russian).

[21] V.R. Barseghyan and T.V. Barseghyan: On an approach to the problems of control of dynamic system with nonseparated multipoint intermediate conditions. Automation and Remote Control, 76(4), (2015), 549–559, DOI: 10.1134/S0005117915040013.

Go to article
[2] A.G Butkovskii, S.A Malyi, and Yu.N. Andreev: Optimal Control of Metal Heating. Moscow, Metallurgy, 1972 (in Russian).

[3] A.I. Egorov: Optimal Control of Thermal and Diffusion Processes. Nauka, 1978 (in Russian).

[4] A.I. Egorov and L.N. Znamenskaya: Introduction to the Theory of Control of Systems with Distributed Parameters. Textbook, Saint Petersburg, LAN, 2017 (in Russian).

[5] E.Ya. Rapoport: Structural Modeling of Objects and Control Systems with Distributed Parameters. Higher School, 2003 (in Russian).

[6] A.N. Tikhonov and A.A. Samarskii: Equations of Mathematical Physics. Nauka, 1977 (in Russian).

[7] V.I. Ukhobotov and I.V. Izmest’ev: A control problem for a rod heating process with unknown temperature at the right end and unknown density of the heat source. Trudy Instituta Matematiki i Mekhaniki, UrO RAN, 25(1), (2019), 297–305 (in Russian), DOI: 10.21538/0134-4889-2019-25-1-297-305.

[8] V.I. Ukhobotov and I.V. Izmest’ev: The problem of controlling the process of heating the rod in the presence of disturbance and uncertainty. IFAC Papers OnLine, 51(32), (2018), 739–742, DOI: 10.1016/j.ifacol.2018.11.458.

[9] V.I. Butyrin and L.A. Fylshtynskyi: Optimal control of the temperature field in the rod when changing the control zone programmatically. Applied Mechanics, 12(84), (1976), 115–118 (in Russian).

[10] M.M. Kopets: Optimal control over the process of heating of a thin core. Reports of the National Academy of Sciences of Ukraine, 7, (2014), 48–52 (in Ukrainian), http://dspace.nbuv.gov.ua/handle/123456789/87951.

[11] N.V.Gybkina, D.Yu. Podusov, and M.V. Sidorov: The optimal control of a homogeneous rod final temperature state. Radioelectronics and Informatics, 2 (2014), 9–15 (in Russian).

[12] E.Y. Vedernikova and A.A. Kornev: To the problem of rod heating. Moscow Univ. Math. Bull., 69, (2014), 237–241, DOI: 10.3103/S0027132214060023.

[13] J.F. Bonnans and P. Jaisson: Optimal control of a parabolic equation with time-dependent state constraints. SIAM Journal on Control and Optimization, 48(7), (2010), 4550–4571.

[14] A. Lapin and E. Laitinen: Iterative solution of mesh constrained optimal control problems with two-level mesh approximations of parabolic state equation. Journal of Applied Mathematics and Physics, 6, (2018), 58–68, DOI: 10.4236/jamp.2018.61007.

[15] K. Kunisch and L. Wang: Time optimal control of the heat equation with pointwise control constraints. ESAIM: Control, Optimisation and Calculus of Variations, 19(2), (2013), 460–485, http://eudml.org/doc/272753.

[16] J.M. Lemos, L. Marreiro, and B. Costa: Supervised multiple model adaptive control of a heating fan. Archives of Control Sciences, 18(1), (2008), 5–16.

[17] S.H. Jilavyan, E.R. Grigoryan, and A.Zh. Khurshudyan: Heating control of a finite rod with a mobile source. Archives of Control Sciences, 31(2), (2021), 417–430, DOI: 10.24425/acs.2021.137425.

[18] V.R. Barseghyan: Control problem of string vibrations with inseparable multipoint conditions at intermediate points in time. Mechanics of Solids, 54(8), (2019), 1216–1226. DOI: 10.3103/S0025654419080120.

[19] V.R. Barseghyan: Optimal control of string vibrations with nonseparate state function conditions at given intermediate instants. Automation and Remote Control, 81(2), (2020), 226–235, DOI: 10.1134/S0005117920020034.

[20] V.R. Barseghyan: Control of Compound Dynamic Systems and of Systems with Multipoint Intermediate Conditions. Nauka, 2016 (in Russian).

[21] V.R. Barseghyan and T.V. Barseghyan: On an approach to the problems of control of dynamic system with nonseparated multipoint intermediate conditions. Automation and Remote Control, 76(4), (2015), 549–559, DOI: 10.1134/S0005117915040013.

The solar photovoltaic output power fluctuates according to solar irradiation, temperature, and load impedance variations. Due to the operating point fluctuations, extracting maximum power from the PV generator, already having a low power conversion ratio, becomes very complicated. To reach a maximum power operating point, a maximum power point tracking technique (MPPT) should be used. Under partial shading condition, the nonlinear PV output power curve contains multiple maximum power points with only one global maximum power point (GMPP). Consequently, identifying this global maximum power point is a difficult task and one of the biggest challenges of partially shaded PV systems. The conventional MPPT techniques can easily be trapped in a local maximum instead of detecting the global one. The artificial neural network techniques used to track the GMPP have a major drawback of using huge amount of data covering all operating points of PV system, including different uniform and non-uniform irradiance cases, different temperatures and load impedances. The biological intelligence techniques used to track GMPP, such as grey wolf algorithm and cuckoo search algorithm (CSA), have two main drawbacks; to be trapped in a local MPP if they have not been well tuned and the precision-transient tracking time complex paradox. To deal with these drawbacks, a Distributive Cuckoo Search Algorithm (DCSA) is developed, in this paper, as GMPP tracking technique. Simulation results of the system for different partial shading patterns demonstrated the high precision and rapidity, besides the good reliability of the proposed DCSAGMPPT technique, compared to the conventional CSA-GMPPT.

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[1] Zhao Zhuoli, Runting Cheng, Baiping Yan, Jiexiong Zhang, Ze- han Zhang, Mingyu Zhang, and Loi Lei Lai: A dynamic particles MPPT method for photovoltaic systems under partial shading conditions. Energy Conversion and Management, 220 (2020), 113070, DOI: 10.1016/j.enconman.2020.113070.

[2] Nabil A. Ahmed and Masafumi Miyatake: A novel maximum power point tracking for photovoltaic applications under partially shaded insolation conditions. Electric Power Systems Research, 78(5), (2008), 777–784, DOI: 10.1016/j.epsr.2007.05.026.

[3] Liqun Liu, Xiaoli Meng, and Chunxia Liu: A review of maximum power point tracking methods of PV power system at uniform and partial shading. Renewable and Sustainable Energy Reviews, 53 (2016), 1500–1507, DOI: 10.1016/j.rser.2015.09.065.

[4] Yanzhi Wang, Xue Lin, Younghyun Kim, Naehyuck Chang, and Mas- soud Pedram: Enhancing efficiency and robustness of a photovoltaic power system under partial shading. Thirteenth International Symposium on Quality Electronic Design (ISQED), Santa Clara USA, (2012), 592–600, DOI: 10.1109/ISQED.2012.6187554.

[5] Ricardo Orduz, Jorge Solorzano, Miguel Ángel Egido, and Ed- uardo Roman: Analytical study and evaluation results of power optimizers for distributed power conditioning in photovoltaic arrays. Progress in Photovoltaics: Research and Applications, 21(3), (2013), 359–373, DOI: 10.1002/pip.1188.

[6] Kashif Ishaque and Zainal Salam: A review of maximum power point tracking techniques of PV system for uniform insolation and partial shading condition. Renewable and Sustainable Energy Reviews, 19 (2013), 475–488, DOI: 10.1016/j.rser.2012.11.032.

[7] Jubaer Ahmed and Zainal Salam: A critical evaluation on maximum power point tracking methods for partial shading in PV systems. Renewable and Sustainable Energy Reviews, 47 (2015), 933–953, DOI: 10.1016/j.rser.2015.03.080.

[8] Ali M. Eltamaly: Performance of MPPT techniques of photovoltaic systems under normal and partial shading conditions. Advances in Renewable Energies and Power Technologies, vol. 1, Solar and Wind Energies, I. Yahyaoui, 2018, Elsevier, Chapter 4, 115–161.

[9] Ali M. Eltamaly: Performance of smart maximum power point tracker under partial shading conditions of photovoltaic systems. Journal ofRenewable and Sustainable Energy, 7(4), (2015), 043141, DOI: 10.1063/1.4929665.

[10] A. Talha, H. Boumaaraf, and O. Bouhali: Evaluation of maximum power point tracking methods for photovoltaic systems. Archives of Control Sciences, 21(2), (2011), 151–165.

[11] Hegazy Rezk and Ali M. Eltamaly: A comprehensive comparison of different MPPT techniques for photovoltaic systems. Solar Energy, 112 (2015), 1–11, DOI: 10.1016/j.solener.2014.11.010.

[12] S. Lyden and M.E. Haque: Maximum power point tracking techniques for photovoltaic systems: A comprehensive review and comparative analysis. Renewable and Sustainable Energy Reviews, 52 (2015): 1504–1518, DOI: 10.1016/j.rser.2015.07.172.

[13] Zainal Salam, Jubaer Ahmed, and Benny S. Merugu: The application of soft computing methods for MPPT of PV system: A technological and status review. Applied Energy, 107 (2013), 135–148, DOI: 10.1016/j.apenergy.2013.02.008.

[14] Hassan M.H. Farh, Mohamed F. Othman, and Ali M. Eltamaly: Maximum power extraction from grid-connected PV system. Saudi Arabia Smart Grid (SASG), (2017), 1–6, DOI: 10.1109/SASG.2017.8356498.

[15] Seyedali Mirjalili, Seyed Mohammad Mirjalili, and Andrew Lewis: GreyWolf optimizer. Advances in Engineering Software, 69 (2014), 46–61, DOI: 10.1016/j.advengsoft.2013.12.007.

[16] Sabrina Titri, Cherif Larbes, Kamal Youcef Toumi, and Karima Be- natchba: A new MPPT controller based on the ant colony optimization algorithm for photovoltaic systems under partial shading conditions. Applied Soft Computing, 58 (2017), 465–479, DOI: 10.1016/j.asoc.2017.05.017.

[17] Lian Lian Jiang, Douglas L. Maskell, and Jagdish C. Patra:Anovel ant colony optimization-based maximum power point tracking for photovoltaic systems under partially shaded conditions. Energy and Buildings, 58 (2013), 227–236, DOI: 10.1016/j.enbuild.2012.12.001.

[18] Lian Lian Jiang, R. Srivatsan, and Douglas L. Maskell: Computational intelligence techniques for maximum power point tracking in PV systems: A review. Renewable and Sustainable Energy Reviews, 85 (2018), 14–45, DOI: 10.1016/j.rser.2018.01.006.

[19] Ali M. Eltamaly and Hassan M.H. Farh: Dynamic global maximum power point tracking of the PV systems under variant partial shading using hybrid GWO-FLC. Solar Energy, 177 (2019), 306–316, DOI: 10.1016/j.solener.2018.11.028.

[20] Jubaer Ahmed and Zainal Salam: A maximum power point tracking (MPPT) for PV system using cuckoo search with partial shading capability. Applied Energy, 119 (2014), 118–130, DOI: 10.1016/j.apenergy.2013.12.062.

[21] Xin-She Yang and Suash Deb: Cuckoo search via Lévy flights. 2009 World Congress on Nature & Biologically Inspired Computing (NaBIC), Coimbatore, India (2009), 210–214, DOI: 10.1109/NABIC.2009.5393690.

[22] Jubaer Ahmed and Zainal Salam: A soft computing MPPT for PV system based on cuckoo search algorithm. 4th International Conference on Power Engineering, Energy and Electrical Drives, Istanbul, Turkey, (2013), 558– 562, DOI: 10.1109/PowerEng.2013.6635669.

[23] Ahmed A. El Baset, A. El Halim, Naggar H. , and Ahmed A. El Sattar: A comparative study between perturb and observe and cuckoo search algorithm for maximum power point tracking. 21st International Middle East Power Systems Conference (MEPCON), Cairo, Egypt, (2019), 716–723, DOI: 10.1109/MEPCON47431.2019.9008210.

[24] Filippo Spertino and Jean Sumaili Akilimali: Are manufacturing I–V mismatch and reverse currents key factors in large photovoltaic arrays? IEEE Transactions on Industrial Electronics, 56(11), (2009), 4520–4531, DOI: 10.1109/TIE.2009.2025712.

[25] M. Drif, P.J. Perez, J. Aguilera, and J.D. Aguilar: A new estimation method of irradiance on a partially shaded PV generator in grid-connected photovoltaic systems. Renewable Energy, 33(9), (2008), 2048–2056, DOI: 10.1016/j.renene.2007.12.010.

[26] Bidyadhar Subudhi and Raseswari Pradhan: A comparative study on maximum power point tracking techniques for photovoltaic power systems. IEEE Transactions on Sustainable Energy, 4(1), (2012), 89–98, DOI: 10.1109/TSTE.2012.2202294.

[27] Kashif Ishaque and Zainal Salam:AcomprehensiveMATLAB Simulink PV system simulator with partial shading capability based on two-diode model. Solar Energy, 85(9), (2011), 2217–2227, DOI: 10.1016/j.solener.2011.06.008.

[28] Mohamed I.Mosaad, M. Osama Abed el-Raouf, Mahmoud A. Al- Ahmar, and Fahd A. Banakher: Maximum power point tracking of PV system based cuckoo search algorithm; review and comparison. Energy Procedia, 162 (2019), 117–126, DOI: 10.1016/j.egypro.2019.04.013.

[29] Bo Yang, JingboWang, Xiaoshun Zhang, Tao Yu, Wei Yao, Hongchun Shu, Fang Zeng, and Liming Sun: Comprehensive overview of metaheuristic algorithm applications on PV cell parameter identification. Energy Conversion and Management, 208 (2020), 112595, DOI: 10.1016/j.enconman.2020.112595.

[30] Tong Kang, Jiangang Yao, Min Jin, Shengjie Yang, and Thanh Long Duong: A novel improved cuckoo search algorithm for parameter estimation of photovoltaic (PV) models. Energies, 11(5), (2018), 1060, DOI: 10.3390/en11051060.

[31] S. Walton, O. Hassan, K. Morgan, and M.R. Brown: Modified cuckoo search: a new gradient free optimisation algorithm. Chaos, Solitons & Fractals, 44(9), (2011), 710718, DOI: 10.1016/j.chaos.2011.06.004.

[32] Amir Hossein Gandomi, Xin-She Yang, and Amir Hossein Alavi: Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems. Engineering with Computers, 29(1), (2013), 17–35, DOI: 10.1007/s00366-011-0241-y.

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[34] Ehsan Valian, Saeed Tavakoli, Shahram Mohanna, and Atiyeh Haghi: Improved cuckoo search for reliability optimization problems. Computers & Industrial Engineering, 64(1), (2013), 459–468, DOI: 10.1016/j.cie.2012.07.011.

[35] Xiangtao Li, Jianan Wang, and Minghao Yin: Enhancing the performance of cuckoo search algorithm using orthogonal learning method. Neural Computing and Applications, 24(6), (2014), 1233–1247, DOI: 10.1007/s00521-013-1354-6.

[36] Hui Wang, Wenjun Wang, Hui Sun, Zhihua Cui, Shahryar Rahna- mayan, and Sanyou Zeng: A new cuckoo search algorithm with hybrid strategies for flow shop scheduling problems. Soft Computing, 21(15), (2017), 4297–4307, DOI: 10.1007/s00500-016-2062-9.

[37] Wang Jianzhou, He Jiang, Yujie Wu, and Yao Dong: Forecasting solar radiation using an optimized hybrid model by cuckoo search algorithm. Energy, 81 (2015), 627–644, DOI: 10.1016/j.energy.2015.01.006.

[38] Wen Long, Shaohong Cai, Jianjun Jiao, Ming Xu, and Tiebin Wu: A new hybrid algorithm based on grey wolf optimizer and cuckoo search for parameter extraction of solar photovoltaic models. Energy Conversion and Management, 203 (2020), 112243, DOI: 10.1016/j.enconman.2019.112243.

[39] Diego Oliva, Ahmed A. Ewees, Mohamed Abd El Aziz, Aboul Ella Hassanien, and Marco Perez-Cisneros: A chaotic improved artificial bee colony for parameter estimation of photovoltaic cells. Energies, 10(7), (2017), 865, DOI: 10.3390/en10070865.

[40] Xiaofang Yuan, Yuqing He, and Liangjiang Liu: Parameter extraction of solar cell models using chaotic asexual reproduction optimization. Neural Computing and Applications, 26(5), (2015), 1227–1239, DOI: 10.1007/s00521-014-1795-6.

[41] Xiaofang Yuan, Yongzhong Xiang, and Yuqing He: Parameter extraction of solar cell models using mutative-scale parallel chaos optimization algorithm. Solar Energy, 108 (2014), 238–251, DOI: 10.1016/j.solener.2014.07.013.

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[43] Santhan Kumar Cherukuri and Srinivasa Rao Rayapudi: Enhanced grey wolf optimizer based MPPT algorithm of PV system under partial shaded condition. International Journal of Renewable Energy Development, 6(3), (2017), 203–212, DOI: 10.14710/ijred.6.3.203-212.

[44] Adeel Feroz Mirza, Qiang Ling, M. Yaqoob Javed, and Majad Man- soor: Novel MPPT techniques for photovoltaic systems under uniform irradiance and Partial shading. Solar Energy, 184 (2019), 628–648, DOI: 10.1016/j.solener.2019.04.034.

Go to article
[2] Nabil A. Ahmed and Masafumi Miyatake: A novel maximum power point tracking for photovoltaic applications under partially shaded insolation conditions. Electric Power Systems Research, 78(5), (2008), 777–784, DOI: 10.1016/j.epsr.2007.05.026.

[3] Liqun Liu, Xiaoli Meng, and Chunxia Liu: A review of maximum power point tracking methods of PV power system at uniform and partial shading. Renewable and Sustainable Energy Reviews, 53 (2016), 1500–1507, DOI: 10.1016/j.rser.2015.09.065.

[4] Yanzhi Wang, Xue Lin, Younghyun Kim, Naehyuck Chang, and Mas- soud Pedram: Enhancing efficiency and robustness of a photovoltaic power system under partial shading. Thirteenth International Symposium on Quality Electronic Design (ISQED), Santa Clara USA, (2012), 592–600, DOI: 10.1109/ISQED.2012.6187554.

[5] Ricardo Orduz, Jorge Solorzano, Miguel Ángel Egido, and Ed- uardo Roman: Analytical study and evaluation results of power optimizers for distributed power conditioning in photovoltaic arrays. Progress in Photovoltaics: Research and Applications, 21(3), (2013), 359–373, DOI: 10.1002/pip.1188.

[6] Kashif Ishaque and Zainal Salam: A review of maximum power point tracking techniques of PV system for uniform insolation and partial shading condition. Renewable and Sustainable Energy Reviews, 19 (2013), 475–488, DOI: 10.1016/j.rser.2012.11.032.

[7] Jubaer Ahmed and Zainal Salam: A critical evaluation on maximum power point tracking methods for partial shading in PV systems. Renewable and Sustainable Energy Reviews, 47 (2015), 933–953, DOI: 10.1016/j.rser.2015.03.080.

[8] Ali M. Eltamaly: Performance of MPPT techniques of photovoltaic systems under normal and partial shading conditions. Advances in Renewable Energies and Power Technologies, vol. 1, Solar and Wind Energies, I. Yahyaoui, 2018, Elsevier, Chapter 4, 115–161.

[9] Ali M. Eltamaly: Performance of smart maximum power point tracker under partial shading conditions of photovoltaic systems. Journal ofRenewable and Sustainable Energy, 7(4), (2015), 043141, DOI: 10.1063/1.4929665.

[10] A. Talha, H. Boumaaraf, and O. Bouhali: Evaluation of maximum power point tracking methods for photovoltaic systems. Archives of Control Sciences, 21(2), (2011), 151–165.

[11] Hegazy Rezk and Ali M. Eltamaly: A comprehensive comparison of different MPPT techniques for photovoltaic systems. Solar Energy, 112 (2015), 1–11, DOI: 10.1016/j.solener.2014.11.010.

[12] S. Lyden and M.E. Haque: Maximum power point tracking techniques for photovoltaic systems: A comprehensive review and comparative analysis. Renewable and Sustainable Energy Reviews, 52 (2015): 1504–1518, DOI: 10.1016/j.rser.2015.07.172.

[13] Zainal Salam, Jubaer Ahmed, and Benny S. Merugu: The application of soft computing methods for MPPT of PV system: A technological and status review. Applied Energy, 107 (2013), 135–148, DOI: 10.1016/j.apenergy.2013.02.008.

[14] Hassan M.H. Farh, Mohamed F. Othman, and Ali M. Eltamaly: Maximum power extraction from grid-connected PV system. Saudi Arabia Smart Grid (SASG), (2017), 1–6, DOI: 10.1109/SASG.2017.8356498.

[15] Seyedali Mirjalili, Seyed Mohammad Mirjalili, and Andrew Lewis: GreyWolf optimizer. Advances in Engineering Software, 69 (2014), 46–61, DOI: 10.1016/j.advengsoft.2013.12.007.

[16] Sabrina Titri, Cherif Larbes, Kamal Youcef Toumi, and Karima Be- natchba: A new MPPT controller based on the ant colony optimization algorithm for photovoltaic systems under partial shading conditions. Applied Soft Computing, 58 (2017), 465–479, DOI: 10.1016/j.asoc.2017.05.017.

[17] Lian Lian Jiang, Douglas L. Maskell, and Jagdish C. Patra:Anovel ant colony optimization-based maximum power point tracking for photovoltaic systems under partially shaded conditions. Energy and Buildings, 58 (2013), 227–236, DOI: 10.1016/j.enbuild.2012.12.001.

[18] Lian Lian Jiang, R. Srivatsan, and Douglas L. Maskell: Computational intelligence techniques for maximum power point tracking in PV systems: A review. Renewable and Sustainable Energy Reviews, 85 (2018), 14–45, DOI: 10.1016/j.rser.2018.01.006.

[19] Ali M. Eltamaly and Hassan M.H. Farh: Dynamic global maximum power point tracking of the PV systems under variant partial shading using hybrid GWO-FLC. Solar Energy, 177 (2019), 306–316, DOI: 10.1016/j.solener.2018.11.028.

[20] Jubaer Ahmed and Zainal Salam: A maximum power point tracking (MPPT) for PV system using cuckoo search with partial shading capability. Applied Energy, 119 (2014), 118–130, DOI: 10.1016/j.apenergy.2013.12.062.

[21] Xin-She Yang and Suash Deb: Cuckoo search via Lévy flights. 2009 World Congress on Nature & Biologically Inspired Computing (NaBIC), Coimbatore, India (2009), 210–214, DOI: 10.1109/NABIC.2009.5393690.

[22] Jubaer Ahmed and Zainal Salam: A soft computing MPPT for PV system based on cuckoo search algorithm. 4th International Conference on Power Engineering, Energy and Electrical Drives, Istanbul, Turkey, (2013), 558– 562, DOI: 10.1109/PowerEng.2013.6635669.

[23] Ahmed A. El Baset, A. El Halim, Naggar H. , and Ahmed A. El Sattar: A comparative study between perturb and observe and cuckoo search algorithm for maximum power point tracking. 21st International Middle East Power Systems Conference (MEPCON), Cairo, Egypt, (2019), 716–723, DOI: 10.1109/MEPCON47431.2019.9008210.

[24] Filippo Spertino and Jean Sumaili Akilimali: Are manufacturing I–V mismatch and reverse currents key factors in large photovoltaic arrays? IEEE Transactions on Industrial Electronics, 56(11), (2009), 4520–4531, DOI: 10.1109/TIE.2009.2025712.

[25] M. Drif, P.J. Perez, J. Aguilera, and J.D. Aguilar: A new estimation method of irradiance on a partially shaded PV generator in grid-connected photovoltaic systems. Renewable Energy, 33(9), (2008), 2048–2056, DOI: 10.1016/j.renene.2007.12.010.

[26] Bidyadhar Subudhi and Raseswari Pradhan: A comparative study on maximum power point tracking techniques for photovoltaic power systems. IEEE Transactions on Sustainable Energy, 4(1), (2012), 89–98, DOI: 10.1109/TSTE.2012.2202294.

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Keywords:
process control
Q-learning algorithm
reinforcement learning
intelligent control
on-line learning

This paper presents how Q-learning algorithm can be applied as a general-purpose selfimproving controller for use in industrial automation as a substitute for conventional PI controller implemented without proper tuning. Traditional Q-learning approach is redefined to better fit the applications in practical control loops, including new definition of the goal state by the closed loop reference trajectory and discretization of state space and accessible actions (manipulating variables). Properties of Q-learning algorithm are investigated in terms of practical applicability with a special emphasis on initializing of Q-matrix based only on preliminary PI tunings to ensure bumpless switching between existing controller and replacing Q-learning algorithm. A general approach for design of Q-matrix and learning policy is suggested and the concept is systematically validated by simulation in the application to control two examples of processes exhibiting first order dynamics and oscillatory second order dynamics. Results show that online learning using interaction with controlled process is possible and it ensures significant improvement in control performance compared to arbitrarily tuned PI controller.

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[1] H. Boubertakh, S. Labiod, M. Tadjine and P.Y. Glorennec: Optimization of fuzzy PID controllers using Q-learning algorithm. Archives of Control Sciences, 18(4), (2008), 415–435

[2] I.Carlucho, M. De Paula, S.A. Villar and G.G.Acosta: Incremental Qlearning strategy for adaptive PID control of mobile robots. Expert Systems With Applications, 80, (2017), 183–199, DOI: 10.1016/j.eswa.2017.03.002.

[3] K. Delchev: Simulation-based design of monotonically convergent iterative learning control for nonlinear systems. Archives of Control Sciences, 22(4), (2012), 467–480.

[4] M. Jelali: An overview of control performance assessment technology and industrial applications. Control Eng. Pract., 14(5), (2006), 441–466, DOI: 10.1016/j.conengprac.2005.11.005.

[5] M. Jelali: Control Performance Management in Industrial Automation: Assessment, Diagnosis and Improvement of Control Loop Performance. Springer-Verlag London, (2013)

[6] H.-K. Lam, Q. Shi, B. Xiao, and S.-H. Tsai: Adaptive PID Controller Based on Q-learning Algorithm. CAAI Transactions on Intelligence Technology, 3(4), (2018), 235–244, DOI: 10.1049/trit.2018.1007.

[7] D. Li, L. Qian, Q. Jin, and T. Tan: Reinforcement learning control with adaptive gain for a Saccharomyces cerevisiae fermentation process. Applied Soft Computing, 11, (2011), 4488–4495, DOI: 10.1016/j.asoc.2011.08.022.

[8] M.M. Noel and B.J. Pandian: Control of a nonlinear liquid level system using a new artificial neural network based reinforcement learning approach. Applied Soft Computing, 23, (2014), 444–451, DOI: 10.1016/j.asoc.2014.06.037.

[9] T. Praczyk: Concepts of learning in assembler encoding. Archives of Control Sciences, 18(3), (2008), 323–337.

[10] M.B. Radac and R.E. Precup: Data-driven model-free slip control of antilock braking systems using reinforcement Q-learning. Neurocomputing, 275, (2017), 317–327, DOI: 10.1016/j.neucom.2017.08.036.

[11] A.K. Sadhu and A. Konar: Improving the speed of convergence of multi-agent Q-learning for cooperative task-planning by a robot-team. Robotics and Autonomous Systems, 92, (2017), 66–80, DOI: 10.1016/j.robot.2017.03.003.

[12] N. Sahebjamnia, R. Tavakkoli-Moghaddam, and N. Ghorbani: Designing a fuzzy Q-learning multi-agent quality control system for a continuous chemical production line – A case study. Computers & Industrial Engineering, 93, (2016), 215–226, DOI: 10.1016/j.cie.2016.01.004.

[13] K. Stebel: Practical aspects for the model-free learning control initialization. in Proc. of 2015 20th International Conference on Methods and Models in Automation and Robotics (MMAR), Poland, (2015), DOI: 10.1109/MMAR.2015.7283918.

[14] R.S. Sutton and A.G. Barto: Reinforcement learning: An Introduction, MIT Press, (1998)

[15] S. Syafiie, F. Tadeo, and E. Martinez: Softmax and "-greedy policies applied to process control. IFAC Proceedings, 37, (2004), 729–734, DOI: 10.1016/S1474-6670(16)31556-2.

[16] S. Syafiie, F. Tadeo, and E. Martinez: Model-free learning control of neutralization process using reinforcement learning. Engineering Applications of Artificial Intelligence, 20, (2007), 767–782, DOI: 10.1016/j.engappai.2006.10.009.

[17] S. Syafiie, F. Tadeo, and E. Martinez: Learning to control pH processes at multiple time scales: performance assessment in a laboratory plant. Chemical Product and Process Modeling, 2(1), (2007), DOI: 10.2202/1934- 2659.1024.

[18] S. Syafiie, F. Tadeo, E. Martinez, and T. Alvarez: Model-free control based on reinforcement learning for a wastewater treatment problem. Applied Soft Computing, 11, (2011), 73–82, DOI: 10.1016/j.asoc.2009.10.018.

[19] P. Van Overschee and B. De Moor: RAPID: The End of Heuristic PID Tuning. IFAC Proceedings, 33(4), (2000), 595–600, DOI: 10.1016/S1474- 6670(16)38308-8.

[20] M. Wang, G. Bian, and H. Li: A new fuzzy iterative learning control algorithm for single joint manipulator. Archives of Control Sciences, 26(3), (2016), 297–310. DOI: 10.1515/acsc-2016-0017.

[21] Ch.J.C.H. Watkins and P. Dayan: Technical Note: Q-learning. Machine Learning, 8, (1992), 279–292, DOI: 10.1023/A:1022676722315.

Go to article
[2] I.Carlucho, M. De Paula, S.A. Villar and G.G.Acosta: Incremental Qlearning strategy for adaptive PID control of mobile robots. Expert Systems With Applications, 80, (2017), 183–199, DOI: 10.1016/j.eswa.2017.03.002.

[3] K. Delchev: Simulation-based design of monotonically convergent iterative learning control for nonlinear systems. Archives of Control Sciences, 22(4), (2012), 467–480.

[4] M. Jelali: An overview of control performance assessment technology and industrial applications. Control Eng. Pract., 14(5), (2006), 441–466, DOI: 10.1016/j.conengprac.2005.11.005.

[5] M. Jelali: Control Performance Management in Industrial Automation: Assessment, Diagnosis and Improvement of Control Loop Performance. Springer-Verlag London, (2013)

[6] H.-K. Lam, Q. Shi, B. Xiao, and S.-H. Tsai: Adaptive PID Controller Based on Q-learning Algorithm. CAAI Transactions on Intelligence Technology, 3(4), (2018), 235–244, DOI: 10.1049/trit.2018.1007.

[7] D. Li, L. Qian, Q. Jin, and T. Tan: Reinforcement learning control with adaptive gain for a Saccharomyces cerevisiae fermentation process. Applied Soft Computing, 11, (2011), 4488–4495, DOI: 10.1016/j.asoc.2011.08.022.

[8] M.M. Noel and B.J. Pandian: Control of a nonlinear liquid level system using a new artificial neural network based reinforcement learning approach. Applied Soft Computing, 23, (2014), 444–451, DOI: 10.1016/j.asoc.2014.06.037.

[9] T. Praczyk: Concepts of learning in assembler encoding. Archives of Control Sciences, 18(3), (2008), 323–337.

[10] M.B. Radac and R.E. Precup: Data-driven model-free slip control of antilock braking systems using reinforcement Q-learning. Neurocomputing, 275, (2017), 317–327, DOI: 10.1016/j.neucom.2017.08.036.

[11] A.K. Sadhu and A. Konar: Improving the speed of convergence of multi-agent Q-learning for cooperative task-planning by a robot-team. Robotics and Autonomous Systems, 92, (2017), 66–80, DOI: 10.1016/j.robot.2017.03.003.

[12] N. Sahebjamnia, R. Tavakkoli-Moghaddam, and N. Ghorbani: Designing a fuzzy Q-learning multi-agent quality control system for a continuous chemical production line – A case study. Computers & Industrial Engineering, 93, (2016), 215–226, DOI: 10.1016/j.cie.2016.01.004.

[13] K. Stebel: Practical aspects for the model-free learning control initialization. in Proc. of 2015 20th International Conference on Methods and Models in Automation and Robotics (MMAR), Poland, (2015), DOI: 10.1109/MMAR.2015.7283918.

[14] R.S. Sutton and A.G. Barto: Reinforcement learning: An Introduction, MIT Press, (1998)

[15] S. Syafiie, F. Tadeo, and E. Martinez: Softmax and "-greedy policies applied to process control. IFAC Proceedings, 37, (2004), 729–734, DOI: 10.1016/S1474-6670(16)31556-2.

[16] S. Syafiie, F. Tadeo, and E. Martinez: Model-free learning control of neutralization process using reinforcement learning. Engineering Applications of Artificial Intelligence, 20, (2007), 767–782, DOI: 10.1016/j.engappai.2006.10.009.

[17] S. Syafiie, F. Tadeo, and E. Martinez: Learning to control pH processes at multiple time scales: performance assessment in a laboratory plant. Chemical Product and Process Modeling, 2(1), (2007), DOI: 10.2202/1934- 2659.1024.

[18] S. Syafiie, F. Tadeo, E. Martinez, and T. Alvarez: Model-free control based on reinforcement learning for a wastewater treatment problem. Applied Soft Computing, 11, (2011), 73–82, DOI: 10.1016/j.asoc.2009.10.018.

[19] P. Van Overschee and B. De Moor: RAPID: The End of Heuristic PID Tuning. IFAC Proceedings, 33(4), (2000), 595–600, DOI: 10.1016/S1474- 6670(16)38308-8.

[20] M. Wang, G. Bian, and H. Li: A new fuzzy iterative learning control algorithm for single joint manipulator. Archives of Control Sciences, 26(3), (2016), 297–310. DOI: 10.1515/acsc-2016-0017.

[21] Ch.J.C.H. Watkins and P. Dayan: Technical Note: Q-learning. Machine Learning, 8, (1992), 279–292, DOI: 10.1023/A:1022676722315.

4
Power system oscillation damping controller design: a novel approach of integrated HHO-PSO algorithm

Keywords:
Harris hawk optimization
Power system stabilizers
STATCOM
FACTS
particle swarm optimization

The hybridization of a recently suggested Harris hawk’s optimizer (HHO) with the traditional particle swarm optimization (PSO) has been proposed in this paper. The velocity function update in each iteration of the PSO technique has been adopted to avoid being trapped into local search space with HHO. The performance of the proposed Integrated HHO-PSO (IHHOPSO) is evaluated using 23 benchmark functions and compared with the novel algorithms and hybrid versions of the neighbouring standard algorithms. Statistical analysis with the proposed algorithm is presented, and the effectiveness is shown in the comparison of grey wolf optimization (GWO), Harris hawks optimizer (HHO), barnacles matting optimization (BMO) and hybrid GWO-PSO algorithms. The comparison in convergence characters with the considered set of optimization methods also presented along with the boxplot. The proposed algorithm is further validated via an emerging engineering case study of controller parameter tuning of power system stability enhancement problem. The considered case study tunes the parameters of STATCOM and power system stabilizers (PSS) connected in a sample power network with the proposed IHHOPSO algorithm. A multi-objective function has been considered and different operating conditions has been investigated in this papers which recommends proposed algorithm in an effective damping of power network oscillations.

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Keywords:
assignment
pole
zero
transfer matrix
linear
positive
system
state feedback

Poles and zeros assignment problem by state feedbacks in positive continuous-time and discrete-time systems is analyzed. It is shown that in multi-input multi-output positive linear systems by state feedbacks the poles and zeros of the transfer matrices can be assigned in the desired positions. In the positive continuous-time linear systems the feedback gain matrix can be chosen as a monomial matrix so that the poles and zeros of the transfer matrices have the desired values if the input matrix B is monomial. In the positive discrete-time linear systems to solve the problem the matrix B can be chosen monomial if and only if in every row and every column of the n x n system matrix A the sum of n-1 its entries is less than one. Key words: assignment, pole, zero, transfer matrix, linear, positive, system, state feedback

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Go to article
[2] L. Farina and S. Rinaldi: Positive Linear Systems: Theory and Applications. J. Wiley & Sons, New York, 2000.

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The basic objective of the research is to construct a difference model of the melt motion. The existence of a solution to the problem is proven in the paper. It is also proven the convergence of the difference problem solution to the original problem solution of the melt motion. The Rothe method is implemented to study the Navier–Stokes equations, which provides the study of the boundary value problems correctness for a viscous incompressible flow both numerically and analytically.

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[2] S.Sh. Kazhikenova, S.N. Shaltaqov, D. Belomestny, and G.S. Shai- hova: Finite difference method implementation for Numerical integration hydrodynamic equations melts. Eurasian Physical Technical Journal, 17(33), (2020), 50–56.

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This paper studies an evacuation problem described by a leader-follower model with bounded confidence under predictive mechanisms. We design a control strategy in such a way that agents are guided by a leader, which follows the evacuation path. The proposed evacuation algorithm is based on Model Predictive Control (MPC) that uses the current and the past information of the system to predict future agents’ behaviors. It can be observed that, with MPC method, the leader-following consensus is obtained faster in comparison to the conventional optimal control technique. The effectiveness of the developed MPC evacuation algorithm with respect to different parameters and different time domains is illustrated by numerical examples.

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[1] H. Abdelgawad and B. Abdulhai: Emergency evacuation planning as a network design problem: A critical review. Transportation Letters: The International Journal of Transportation Research, 1 (2009), 41–58, DOI: 10.3328/TL.2009.01.01.41-58.

[2] R. Alizadeh: A dynamic cellular automaton model for evacuation process with obstacles, Safety Science, 49(2), (2011), 315–323, DOI: 10.1016/j.ssci.2010.09.006.

[3] R. Almeida, E. Girejko, L. Machado, A.B. Malinowska, and N. Mar- tins: Application of predictive control to the Hegselmann-Krause model, Mathematical Methods in the Applied Sciences, 41(18), (2018), 9191–9202, DOI: 10.10022Fmma.5132.

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[6] V.D. Blondel, J.M. Hendrickx, and J.N. Tsitsiklis: On Krause’s multiagent consensus model with state-dependent connectivity, IEEE Transactions on Automatics Control, vol. 54(11), (2009), 2586–2597, DOI: 10.1109/TAC.2009.2031211.

[7] V.D. Blondel, J.M. Hendrickx, and J.N. Tsitsiklis: Continuous-time average-preserving opinion dynamics with opinion-dependent communications, SIAM Journal on Control and Optimization, vol. 48(8), (2010), 5214–5240, DOI: 10.1137/090766188.

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[10] E. Girejko, L. Machado, A.B. Malinowska, and N. Martins: Krause’s model of opinion dynamics on isolated time scales, Mathematical Methods in the Applied Sciences, 39 (2016), 5302–5314, DOI: 10.1002/mma.3916.

[11] R. Hegselmann and U. Krause: Opinion dynamics and bounded confidence models, analysis, and simulation, Journal of Artificial Societies and Social Simulation, 5(3), (2002), http://jasss.soc.surrey.ac.uk/5/3/2.html.

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[13] R. Hilscher and V. Zeidan:Weak maximum principle and accessory problem for control problems on time scales, Nonlinear Analysis, 70(9), (2009), 3209–3226, DOI: 10.1016/j.na.2008.04.025.

[14] L. Huang, S.C.Wong, M. Zhang, C.-W. Shu, andW.H.K. Lam: Revisiting Hughes’ dynamics continuum model for pedestrian flow and the development of an efficient solution algorithm, Transportation Research Part B: Methodological, 43(1), (2009), 127–141, DOI: 10.1016/j.trb.2008.06.003.

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[16] R. Lohner: On the modeling of pedestrian motion, Applied Mathematical Modeling, 34(2), (2010), 366–382, DOI: 10.1016/j.apm.2009.04.017.

[17] S.J. Qin and T.A. Badgwell: An Overview of Nonlinear Model Predictive Control Applications, Allgöwer F., Zheng A. ed., ser. Nonlinear Model Predictive Control. Progress in Systems and Control Theory. Birkhäuser, Basel, 2000, vol. 26, pp. 369–392.

[18] S. Wojnar, T. Poloni, P. Šimoncic, B. Rohal’-Ilkiv, M. Honek (and) J. Csambál: Real-time implementation of multiple model based predictive control strategy to air/fuel ratio of a gasoline engine. Archives of Control Sciences, 23(1), (2013), 93–106.

[19] S. Daniar, M. Shiroei and R. Aazami: Multivariable predictive control considering time delay for load-frequency control in multi-area power systems. Archives of Control Sciences, 26(4), (2016), 527–549, DOI: 10.1515/acsc-2016-0029.

[20] Y. Yang, D.V. Dimarogonas, and X. Hu: Optimal leader-follower control for crowd evacuation, Proc. 52nd IEEE Conf. Decision Control (CDC), (2013), 2769–2774, DOI: 10.1109/CDC.2013.6760302.

[21] Z. Zainuddin and M. Shuaib: Modification of the decision-making capability in the social force model for the evacuation process, Transport Theory and Statistical Physics, 39(1), (2011), 47–70, DOI: 10.1080/00411450.2010.529979.

[22] H.-T. Zhang, M.Z. Chen, G.-B. Stan, and T. Zhou: Ultrafast consensus via predictive mechanisms, Europhysics Letters, 83, (2008), no. 40003.

[23] H.-T. Zhang, M.Z. Chen, G.-B. Stan, T. Zhou, and J.M.Maciejowski: Collective behaviour coordination with predictive mechanisms, IEEE Circuits Systems Magazine, 8, (2008) 67–85, DOI: 10.1109/MCAS.2008.928446.

[24] L. Zhang, J. Wang, and Q. Shi: Multi-agent based modeling and simulating for evacuation process in stadium, Journal of Systems Science and Complexity, 27(3), (2014), 430–444, DOI: 10.1007/s11424-014-3029-5.

[25] Y. Zheng, B. Jia, X.-G. Li, and N. Zhu: Evacuation dynamics with fire spreading based on cellular automaton, Physica A: Statistical Mechanics and Its Applications, 390(18-19), (2011), 3147–3156, DOI: 10.1016/j.physa.2011.04.011.

Go to article
[2] R. Alizadeh: A dynamic cellular automaton model for evacuation process with obstacles, Safety Science, 49(2), (2011), 315–323, DOI: 10.1016/j.ssci.2010.09.006.

[3] R. Almeida, E. Girejko, L. Machado, A.B. Malinowska, and N. Mar- tins: Application of predictive control to the Hegselmann-Krause model, Mathematical Methods in the Applied Sciences, 41(18), (2018), 9191–9202, DOI: 10.10022Fmma.5132.

[4] B. Aulbach and S. Hilger: A unified approach to continuous and discrete dynamics, ser. Colloq. Math. Soc. Janos Bolyai, vol. 53, North-Holland, Amsterdam, 1990.

[5] H. Bi and E. Gelenbe: A survey of algorithms and systems for evacuating people in confined spaces, Electronics, 2019 8(6), (2019), 711, DOI: 10.3390/electronics8060711.

[6] V.D. Blondel, J.M. Hendrickx, and J.N. Tsitsiklis: On Krause’s multiagent consensus model with state-dependent connectivity, IEEE Transactions on Automatics Control, vol. 54(11), (2009), 2586–2597, DOI: 10.1109/TAC.2009.2031211.

[7] V.D. Blondel, J.M. Hendrickx, and J.N. Tsitsiklis: Continuous-time average-preserving opinion dynamics with opinion-dependent communications, SIAM Journal on Control and Optimization, vol. 48(8), (2010), 5214–5240, DOI: 10.1137/090766188.

[8] M. Bohner and A. Peterson: Dynamic equations on time scales, Boston, MA: Birkhäuser Boston, 2001.

[9] R.M. Colombo and M. D. Rosini: Pedestrian flows and non-classical shocks, Mathematical Methods in the Applied Sciences, 28(13), (2005), 1553–1567, DOI: 10.1002/mma.624.

[10] E. Girejko, L. Machado, A.B. Malinowska, and N. Martins: Krause’s model of opinion dynamics on isolated time scales, Mathematical Methods in the Applied Sciences, 39 (2016), 5302–5314, DOI: 10.1002/mma.3916.

[11] R. Hegselmann and U. Krause: Opinion dynamics and bounded confidence models, analysis, and simulation, Journal of Artificial Societies and Social Simulation, 5(3), (2002), http://jasss.soc.surrey.ac.uk/5/3/2.html.

[12] D. Helbing and P. Molnar: Social force model for pedestrian dynamics, Physical Review E, 51(5), (1995), 4282–4286, DOI: 10.1103/Phys-RevE.51.4282.

[13] R. Hilscher and V. Zeidan:Weak maximum principle and accessory problem for control problems on time scales, Nonlinear Analysis, 70(9), (2009), 3209–3226, DOI: 10.1016/j.na.2008.04.025.

[14] L. Huang, S.C.Wong, M. Zhang, C.-W. Shu, andW.H.K. Lam: Revisiting Hughes’ dynamics continuum model for pedestrian flow and the development of an efficient solution algorithm, Transportation Research Part B: Methodological, 43(1), (2009), 127–141, DOI: 10.1016/j.trb.2008.06.003.

[15] R.L. Hughes: A continuum theory for the flow of pedestrians, Transportation Research Part B: Methodological, 36(6), (2002), 507–535, DOI: 10.1016/S0191-2615(01)00015-7.

[16] R. Lohner: On the modeling of pedestrian motion, Applied Mathematical Modeling, 34(2), (2010), 366–382, DOI: 10.1016/j.apm.2009.04.017.

[17] S.J. Qin and T.A. Badgwell: An Overview of Nonlinear Model Predictive Control Applications, Allgöwer F., Zheng A. ed., ser. Nonlinear Model Predictive Control. Progress in Systems and Control Theory. Birkhäuser, Basel, 2000, vol. 26, pp. 369–392.

[18] S. Wojnar, T. Poloni, P. Šimoncic, B. Rohal’-Ilkiv, M. Honek (and) J. Csambál: Real-time implementation of multiple model based predictive control strategy to air/fuel ratio of a gasoline engine. Archives of Control Sciences, 23(1), (2013), 93–106.

[19] S. Daniar, M. Shiroei and R. Aazami: Multivariable predictive control considering time delay for load-frequency control in multi-area power systems. Archives of Control Sciences, 26(4), (2016), 527–549, DOI: 10.1515/acsc-2016-0029.

[20] Y. Yang, D.V. Dimarogonas, and X. Hu: Optimal leader-follower control for crowd evacuation, Proc. 52nd IEEE Conf. Decision Control (CDC), (2013), 2769–2774, DOI: 10.1109/CDC.2013.6760302.

[21] Z. Zainuddin and M. Shuaib: Modification of the decision-making capability in the social force model for the evacuation process, Transport Theory and Statistical Physics, 39(1), (2011), 47–70, DOI: 10.1080/00411450.2010.529979.

[22] H.-T. Zhang, M.Z. Chen, G.-B. Stan, and T. Zhou: Ultrafast consensus via predictive mechanisms, Europhysics Letters, 83, (2008), no. 40003.

[23] H.-T. Zhang, M.Z. Chen, G.-B. Stan, T. Zhou, and J.M.Maciejowski: Collective behaviour coordination with predictive mechanisms, IEEE Circuits Systems Magazine, 8, (2008) 67–85, DOI: 10.1109/MCAS.2008.928446.

[24] L. Zhang, J. Wang, and Q. Shi: Multi-agent based modeling and simulating for evacuation process in stadium, Journal of Systems Science and Complexity, 27(3), (2014), 430–444, DOI: 10.1007/s11424-014-3029-5.

[25] Y. Zheng, B. Jia, X.-G. Li, and N. Zhu: Evacuation dynamics with fire spreading based on cellular automaton, Physica A: Statistical Mechanics and Its Applications, 390(18-19), (2011), 3147–3156, DOI: 10.1016/j.physa.2011.04.011.

Keywords:
interval-valued q-rung dual hesitant fuzzy set
Maclaurin symmetric mean operator
multi-criteria decision-making
aggregation operators

In modern society, people concern more about the evaluation of medical service quality. Evaluation of medical service quality is helpful for medical service providers to supervise and improve their service quality. Also, it will help the public to understand the situation of different medical providers. As a multi-criteria decision-making (MCDM) problem, evaluation of medical service quality can be effectively solved by aggregation operators in interval-valued q-rung dual hesitant fuzzy (IVq-RDHF) environment. Thus, this paper proposes interval-valued q-rung dual hesitant Maclaurin symmetric mean (IVq-RDHFMSM) operator and interval-valued q-rung dual hesitant weighted Maclaurin symmetric mean (IVq-RDHFWMSM) operator. Based on the proposed IVq-RDHFWMSM operator, this paper builds a novel approach to solve the evaluation problem of medical service quality including a criteria framework for the evaluation of medical service quality and a novel MCDM method. What’s more, aiming at eliminating the discordance between decision information and weight vector of criteria determined by decisionmakers (DMs), this paper proposes the concept of cross-entropy and knowledge measure in IVq-RDHF environment to extract weight vector from DMs’ decision information. Finally, this paper presents a numerical example of the evaluation of medical service for hospitals to illustrate the availability of the novel method and compares our method with other MCDM methods to demonstrate the superiority of our method. According to the comparison result, our method has more advantages than other methods.

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[51] L. Li and W. Benton: Hospital capacity management decisions: Emphasis on cost control and quality enhancement. European Journal of Operational Research, 146(3), (2003), 596–614, DOI: 10.1016/S0377-2217(02)00225-4.

[52] C. Tian, Y. Tian, and L. Zhang: An evaluation scale of medical services quality based on “patients’ experience”. Journal of Huazhong University of Science and Technology [Medical Sciences], 34, (2014), 289–297, DOI: 10.1007/s11596-014-1273-5.

[53] S. Das, B. Dutta, and De. Guha: Weight computation of criteria in a decision-making problem by knowledge measure with intuitionistic fuzzy set and interval-valued intuitionistic fuzzy set. Soft Computing, 20(9), (2016), 3421–3442, DOI: 10.1007/s00500-015-1813-3.

[54] W. Zhang, X. Li, and Y. Ju: Some aggregation operators based on Einstein operations under interval-valued dual hesitant fuzzy setting and their application. Mathematical Problems in Engineering, 1, (2014), DOI: 10.1155/2014/958927.

[55] K. Rahman, S. Abdullah, M. Shakeel, M.S. Khan, and M. Ullah: Interval-valued Pythagorean fuzzy geometric aggregation operators and their application to group decision making problem. Cogent Mathematics, 4, (2017), DOI: 10.1080/23311835.2017.1338638.

[56] Y. Zang, X. Zhao, and S. Li: Interval-valued dual hesitant fuzzy Heronian mean aggregation operators and their application to multi-attribute decision making, International Journal of Computational Intelligence and Applications, 17(4), (2018), DOI: 10.1142/S1469026818500050.

[57] J. Wang, X. Shang, X. Feng, and M. Sun: A novel multiple attribute decision making method based on q-rung dual hesitant uncertain linguistic sets and Muirhead mean. Archives of Control Sciences, 30(2), (2020), 233– 272, DOI: 10.24425/acs.2020.133499.

[58] L. Li, R. Zhang, J. Wang, and X. Shang: Some q-orthopair linguistic Heronian mean operators with their application to multi-attribute group decision making. Archives of Control Sciences, 28(4), (2018), 551–583, DOI: 10.24425/acs.2018.125483.

[59] A. Biswas and A. Sarkar: Development of dual hesitant fuzzy prioritized operators based on Einstein operations with their application to multicriteria group decision making. Archives of Control Sciences, 28(4), (2018), 527–549, DOI: 10.24425/acs.2018.125482.

Go to article
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[49] W. Yang and Y. Pang: Hesitant interval-valued Pythagorean fuzzy VIKOR method. International Journal of Intelligent Systems, 34(5), (2018), 754– 789, DOI: 10.1002/int.22075.

[50] H. Hiidenhovi, P. Laippala, and K. Nojonen: Development of a patientorientated instrument to measure service quality in outpatient departments. Journal of Advanced Nursing, 34(5), (2001), 696–705, DOI: 10.1046/j.1365-2648.2001.01799.x.

[51] L. Li and W. Benton: Hospital capacity management decisions: Emphasis on cost control and quality enhancement. European Journal of Operational Research, 146(3), (2003), 596–614, DOI: 10.1016/S0377-2217(02)00225-4.

[52] C. Tian, Y. Tian, and L. Zhang: An evaluation scale of medical services quality based on “patients’ experience”. Journal of Huazhong University of Science and Technology [Medical Sciences], 34, (2014), 289–297, DOI: 10.1007/s11596-014-1273-5.

[53] S. Das, B. Dutta, and De. Guha: Weight computation of criteria in a decision-making problem by knowledge measure with intuitionistic fuzzy set and interval-valued intuitionistic fuzzy set. Soft Computing, 20(9), (2016), 3421–3442, DOI: 10.1007/s00500-015-1813-3.

[54] W. Zhang, X. Li, and Y. Ju: Some aggregation operators based on Einstein operations under interval-valued dual hesitant fuzzy setting and their application. Mathematical Problems in Engineering, 1, (2014), DOI: 10.1155/2014/958927.

[55] K. Rahman, S. Abdullah, M. Shakeel, M.S. Khan, and M. Ullah: Interval-valued Pythagorean fuzzy geometric aggregation operators and their application to group decision making problem. Cogent Mathematics, 4, (2017), DOI: 10.1080/23311835.2017.1338638.

[56] Y. Zang, X. Zhao, and S. Li: Interval-valued dual hesitant fuzzy Heronian mean aggregation operators and their application to multi-attribute decision making, International Journal of Computational Intelligence and Applications, 17(4), (2018), DOI: 10.1142/S1469026818500050.

[57] J. Wang, X. Shang, X. Feng, and M. Sun: A novel multiple attribute decision making method based on q-rung dual hesitant uncertain linguistic sets and Muirhead mean. Archives of Control Sciences, 30(2), (2020), 233– 272, DOI: 10.24425/acs.2020.133499.

[58] L. Li, R. Zhang, J. Wang, and X. Shang: Some q-orthopair linguistic Heronian mean operators with their application to multi-attribute group decision making. Archives of Control Sciences, 28(4), (2018), 551–583, DOI: 10.24425/acs.2018.125483.

[59] A. Biswas and A. Sarkar: Development of dual hesitant fuzzy prioritized operators based on Einstein operations with their application to multicriteria group decision making. Archives of Control Sciences, 28(4), (2018), 527–549, DOI: 10.24425/acs.2018.125482.

Keywords:
multiobjective fractional control problem
geodesic efficient solution
(p; b)-geodesic quasiinvexity

In this paper, we introduce necessary and sufficient efficiency conditions associated with a class of multiobjective fractional variational control problems governed by geodesic quasiinvex multiple integral functionals and mixed constraints containing *m*-flow type PDEs. Using the new notion of ( *normal*) *geodesic efficient solution*, under ( *p*; *b*)-geodesic quasiinvexity assumptions, we establish sufficient efficiency conditions for a feasible solution.

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[1] R.P. Agarwal, I. Ahmad, A. Iqbal, and S. Ali: Generalized invex sets and preinvex functions on Riemannian manifolds, Taiwanese J. Math., 16(5), (2012), 1719–1732, DOI: 10.11650/twjm/1500406792.

[2] T. Antczak: G-pre-invex functions in mathematical programming, J. Comput. Appl. Math., 217(1), (2008), 212–226, DOI: 10.1016/j.cam.2007.06.026.

[3] M. Arana-Jimenez, B. Hernandez-Jimenez, G. Ruiz-Garzon, and A. Rufian-Lizana: FJ-invex control problem, Appl. Math. Lett., 22(12), (2009), 1887–1891, DOI: 10.1016/j.aml.2009.07.016.

[4] A. Barani and M.R. Pouryayevali: Invex sets and preinvex functions on Riemannian manifolds, J. Math. Anal. Appl., 328(2), (2007), 767–779, DOI: 10.1016/j.jmaa.2006.05.081.

[5] M.A. Hanson: On sufficiency of Kuhn-Tucker conditions, J. Math. Anal. Appl., 80(2), (1981), 545–550, DOI: 10.1016/0022-247X(81)90123-2.

[6] R. Jagannathan: Duality for nonlinear fractional programs, Z. Oper. Res., 17(1-3), (1973), DOI: 10.1007/BF01951364.

[7] V. Jeyakumar: Strong and weak invexity in mathematical programming, Research report (University of Melbourne, Department of Mathematics), 1984, no. 29.

[8] D.H. Martin: The essence of invexity, J. Optim. Theory Appl., 47(1), (1985), 65–76, DOI: 10.1007/BF00941316.

[9] St. Mititelu: Optimality and duality for invex multi-time control problems with mixed constraints, J. Adv. Math. Stud., 2(1), (2009), 25–34.

[10] St. Mititelu, M.Constantinescu, and C. Udriste: Efficiency for multitime variational problems with geodesic quasiinvex functionals on Riemannian manifolds, BSG Proceedings 22. The Intern. Conf. “Differential Geometry – Dynamical Systems”, September 1-4, 2014, Mangalia-Romania, pp. 38–50. Balkan Society of Geometers, Geometry Balkan Press 2015.

[11] St. Mititelu and S. Treanta: Efficiency conditions in vector control problems governed by multiple integrals, J. Appl. Math. Comput., 57(1-2), (2018), 647–665, DOI: 10.1007/s12190-017-1126-z.

[12] M.A. Noor and K.I. Noor: Some characterizations of strongly preinvex functions, J. Math. Anal. Appl., 316(2), (2006), 697–706, DOI: 10.1016/ j.jmaa.2005.05.014.

[13] V.A. de Oliveira and G.N. Silva: On sufficient optimality conditions for multiobjective control problems, J. Global Optim., 64(4), (2016), 721–744, DOI: 10.1007/s10898-015-0351-y.

[14] R. Pini: Convexity along curves and indunvexity, Optimization, 29(4), (1994), 301–309, DOI: 10.1080/02331939408843959.

[15] T. Rapcsak: Smooth Nonlinear Optimization in Rn, Nonconvex Optimization and Its Applications, Kluwer Academic, 1997.

[16] W. Tang and X. Yang: The sufficiency and necessity conditions of strongly preinvex functions, OR Transactions, 10, 3, (2006), 50–58. [17] S. Treanta: PDEs of Hamilton-Pfaff type via multi-time optimization problems, U.P.B. Sci. Bull., Series A: Appl. Math. Phys., 76(1), (2014), 163–168.

[18] S. Treanta: Optimal control problems on higher order jet bundles. The Intern. Conf. “Differential Geometry – Dynamical Systems”, October 10- 13, 2013, Bucharest-Romania, pp. 181–192. Balkan Society of Geometers, Geometry Balkan Press 2014.

[19] S. Treanta: Multiobjective fractional variational problem on higherorder jet bundles, Commun. Math. Stat., 4(3), (2016), 323–340, DOI: 10.1007/s40304-016-0087-0.

[20] S. Treanta: Higher-order Hamilton dynamics and Hamilton-Jacobi divergence PDE, Comput. Math. Appl., 75(2), (2018), 547–560, DOI: 10.1016/j.camwa.2017.09.033.

[21] S. Treanta and M. Arana-Jimenez: KT-pseudoinvex multidimensional control problem, Optim. Control Appl. Meth., 39(4), (2018), 1291–1300, DOI: 10.1002/oca.2410.

[22] S. Treanta and M. Arana-Jimenez: On generalized KT-pseudoinvex control problems involving multiple integral functionals, Eur. J. Control, 43, (2018), 39–45, DOI: 10.1016/j.ejcon.2018.05.004.

[23] S. Treanta: Efficiency in generalized V-KT-pseudoinvex control problems, Int. J. Control, 93(3), (2020), 611–618, DOI: 10.1080/00207179.2018.1483082.

[24] C. Udriste: Convex Functions and Optimization Methods on Riemannian Manifolds, Mathematics and Its Applications, KluwerAcademic, 297, 1994.

[25] T. Weir and B. Mond: Pre-invex functions in multiple objective optimization, J. Math. Anal. Appl., 136(1), (1988), 29–38, DOI: 10.1016/0022-247X(88)90113-8.

Go to article
[2] T. Antczak: G-pre-invex functions in mathematical programming, J. Comput. Appl. Math., 217(1), (2008), 212–226, DOI: 10.1016/j.cam.2007.06.026.

[3] M. Arana-Jimenez, B. Hernandez-Jimenez, G. Ruiz-Garzon, and A. Rufian-Lizana: FJ-invex control problem, Appl. Math. Lett., 22(12), (2009), 1887–1891, DOI: 10.1016/j.aml.2009.07.016.

[4] A. Barani and M.R. Pouryayevali: Invex sets and preinvex functions on Riemannian manifolds, J. Math. Anal. Appl., 328(2), (2007), 767–779, DOI: 10.1016/j.jmaa.2006.05.081.

[5] M.A. Hanson: On sufficiency of Kuhn-Tucker conditions, J. Math. Anal. Appl., 80(2), (1981), 545–550, DOI: 10.1016/0022-247X(81)90123-2.

[6] R. Jagannathan: Duality for nonlinear fractional programs, Z. Oper. Res., 17(1-3), (1973), DOI: 10.1007/BF01951364.

[7] V. Jeyakumar: Strong and weak invexity in mathematical programming, Research report (University of Melbourne, Department of Mathematics), 1984, no. 29.

[8] D.H. Martin: The essence of invexity, J. Optim. Theory Appl., 47(1), (1985), 65–76, DOI: 10.1007/BF00941316.

[9] St. Mititelu: Optimality and duality for invex multi-time control problems with mixed constraints, J. Adv. Math. Stud., 2(1), (2009), 25–34.

[10] St. Mititelu, M.Constantinescu, and C. Udriste: Efficiency for multitime variational problems with geodesic quasiinvex functionals on Riemannian manifolds, BSG Proceedings 22. The Intern. Conf. “Differential Geometry – Dynamical Systems”, September 1-4, 2014, Mangalia-Romania, pp. 38–50. Balkan Society of Geometers, Geometry Balkan Press 2015.

[11] St. Mititelu and S. Treanta: Efficiency conditions in vector control problems governed by multiple integrals, J. Appl. Math. Comput., 57(1-2), (2018), 647–665, DOI: 10.1007/s12190-017-1126-z.

[12] M.A. Noor and K.I. Noor: Some characterizations of strongly preinvex functions, J. Math. Anal. Appl., 316(2), (2006), 697–706, DOI: 10.1016/ j.jmaa.2005.05.014.

[13] V.A. de Oliveira and G.N. Silva: On sufficient optimality conditions for multiobjective control problems, J. Global Optim., 64(4), (2016), 721–744, DOI: 10.1007/s10898-015-0351-y.

[14] R. Pini: Convexity along curves and indunvexity, Optimization, 29(4), (1994), 301–309, DOI: 10.1080/02331939408843959.

[15] T. Rapcsak: Smooth Nonlinear Optimization in Rn, Nonconvex Optimization and Its Applications, Kluwer Academic, 1997.

[16] W. Tang and X. Yang: The sufficiency and necessity conditions of strongly preinvex functions, OR Transactions, 10, 3, (2006), 50–58. [17] S. Treanta: PDEs of Hamilton-Pfaff type via multi-time optimization problems, U.P.B. Sci. Bull., Series A: Appl. Math. Phys., 76(1), (2014), 163–168.

[18] S. Treanta: Optimal control problems on higher order jet bundles. The Intern. Conf. “Differential Geometry – Dynamical Systems”, October 10- 13, 2013, Bucharest-Romania, pp. 181–192. Balkan Society of Geometers, Geometry Balkan Press 2014.

[19] S. Treanta: Multiobjective fractional variational problem on higherorder jet bundles, Commun. Math. Stat., 4(3), (2016), 323–340, DOI: 10.1007/s40304-016-0087-0.

[20] S. Treanta: Higher-order Hamilton dynamics and Hamilton-Jacobi divergence PDE, Comput. Math. Appl., 75(2), (2018), 547–560, DOI: 10.1016/j.camwa.2017.09.033.

[21] S. Treanta and M. Arana-Jimenez: KT-pseudoinvex multidimensional control problem, Optim. Control Appl. Meth., 39(4), (2018), 1291–1300, DOI: 10.1002/oca.2410.

[22] S. Treanta and M. Arana-Jimenez: On generalized KT-pseudoinvex control problems involving multiple integral functionals, Eur. J. Control, 43, (2018), 39–45, DOI: 10.1016/j.ejcon.2018.05.004.

[23] S. Treanta: Efficiency in generalized V-KT-pseudoinvex control problems, Int. J. Control, 93(3), (2020), 611–618, DOI: 10.1080/00207179.2018.1483082.

[24] C. Udriste: Convex Functions and Optimization Methods on Riemannian Manifolds, Mathematics and Its Applications, KluwerAcademic, 297, 1994.

[25] T. Weir and B. Mond: Pre-invex functions in multiple objective optimization, J. Math. Anal. Appl., 136(1), (1988), 29–38, DOI: 10.1016/0022-247X(88)90113-8.

Keywords:
solar PV array
VSC
SMO
DC-DC converter
lattice Levenberg–Marquardt recursive least squares
hysteresis current controller

This paper presents a new grid integration control scheme that employs spider monkey optimization technique for maximum power point tracking and Lattice Levenberg Marquardt Recursive estimation with a hysteresis current controller for controlling voltage source inverter. This control scheme is applied to a PV system integrated to a three phase grid to achieve effective grid synchronization. To verify the efficacy of the proposed control scheme, simulations were performed. From the simulation results it is observed that the proposed controller provides excellent control performance such as reducing THD of the grid current to 1.75%.

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[1] I. Dincer: Renewable energy and sustainable development: a crucial review. Renewable and Sustainable Energy Reviews, 4(2), (2000), 157–175, DOI: 10.1016/S1364-0321(99)00011-8.

[2] S. Gulkowski, J.V.M. Diez, J.A. Tejero, and G. Nofuentes: Computational modeling and experimental analysis of heterojunction with intrinsic thin-layer photovoltaic module under different environmental conditions. Energy, 172, (2019), 380–390, DOI: 10.1016/j.energy.2019.01.107.

[3] M. Bahrami, et al.: Hybrid maximum power point tracking algorithm with improved dynamic performance. Renewable Energy, 130, (2019), 982–991, DOI: 10.1016/j.renene.2018.07.020.

[4] K.V. Singh, Krishna, H. Bansal, and D. Singh: A comprehensive review on hybrid electric vehicles: architectures and components. Journal of Modern Transportation, 27, (2019), 1–31, DOI: 10.1007/s40534-019-0184-3.

[5] S. Pradhan, et al.: Performance Improvement of Grid-Integrated Solar PV System Using DNLMS Control Algorithm. IEEE Transactions on Industry Applications, 55(1), (2019), 78–91, DOI: 10.1109/TIA.2018.2863652.

[6] S. Negari and D. Xu: Utilizing a Lagrangian approach to compute maximum fault current in hybrid AC–DC distribution grids withMMCinterface. High Voltage, 4(1), (2019), 18–27, DOI: 10.1049/hve.2018.5087.

[7] V.T. Tran et al.: Mitigation of Solar PV Intermittency Using Ramp-Rate Control of Energy Buffer Unit. IEEE Transactions on Energy Conversion, 34(1), (2019), 435–445, DOI: 10.1109/TEC.2018.2875701.

[8] A. Kihal, et al.: An improved MPPT scheme employing adaptive integral derivative sliding mode control for photovoltaic systems under fast irradiation changes. ISA Transactions, 87, (2019), 297–306, DOI: 10.1016/j.isatra.2018.11.020.

[9] A.M. Jadhav, N.R. Patne, and J.M. Guerrero: A novel approach to neighborhood fair energy trading in a distribution network of multiple microgrid clusters. IEEE Transactions on Industrial Electronics, 66(2), (2019), 1520– 1531, DOI: 10.1109/TIE.2018.2815945.

[10] A. Fragaki, T. Markvart, and G. Laskos: All UK electricity supplied by wind and photovoltaics – The 30–30 rule. Energy, 169, (2019), 228–237, DOI: 10.1016/j.energy.2018.11.151.

[11] S.Z. Ahmed, et al.: Power quality enhancement by using D-FACTS systems applied to distributed generation. International Journal of Power Electronics and Drive Systems, 10(1), (2019), 330, DOI: 10.11591/ijpeds.v10.i1.pp330-341.

[12] H.H. Alhelou, et al.: A Survey on Power System Blackout and Cascading Events: Research Motivations and Challenges. Energies. 12(4), (2019), 1– 28, DOI: 10.3390/en12040682.

[13] M. Badoni, A. Singh, and B. Singh: Implementation of Immune Feedback Control Algorithm for Distribution Static Compensator. IEEE Transactions on Industry Applications, 55(1), (2019), 918–927, DOI: 10.1109/TIA.2018.2867328.

[14] S.R. Das, et al.: Performance evaluation of multilevel inverter based hybrid active filter using soft computing techniques. Evolutionary Intelligence (2019), 1–11, DOI: 10.1007/s12065-019-00217-6.

[15] F. Chishti, S. Murshid, and B. Singh: LMMN Based Adaptive Control for Power Quality Improvement of Grid Intertie Wind-PV System. IEEE Transactions on Industrial Informatics, 15(9), (2019), 4900–4912, DOI: 10.1109/TII.2019.2897165.

[16] S. Pradhan, et al.: Performance Improvement of Grid-Integrated Solar PV System Using DNLMS Control Algorithm. IEEE Transactions on Industry Applications, 55(1), (2019), 78–91, DOI: 10.1109/IICPE.2016.8079455.

[17] V. Jain, I. Hussain, and B. Singh: A HTF-Based Higher-Order Adaptive Control of Single-Stage Grid-Interfaced PV System. IEEE Transactions on Industry Applications, 55(2), (2019), 1873–1881, DOI: 10.1109/TIA.2018.2878186.

[18] N. Kumar, B. Singh, B. Ketan Panigrahi and L. Xu: Leaky Least Logarithmic Absolute Difference Based Control Algorithm and Learning Based InC MPPT Technique for Grid Integrated PV System. IEEE Transactions on Industrial Electronics. 66(11), (2019), 9003–9012, DOI: 10.1109/TIE.2018.2890497.

[19] P. Shah, I. Hussain, and B. Singh: Single-Stage SECS Interfaced with Grid Using ISOGI-FLL- Based Control Algorithm. IEEE Transactions on Industry Applications, 55(1), (2019), 701–711, DOI: 10.1109/TIA.2018.2869880.

[20] V. Jain and B. Singh: A Multiple Improved Notch Filter-Based Control for a Single-StagePVSystem Tied to aWeak Grid. IEEE Transactions on Sustainable Energy, 10(1), (2019), 238–247, DOI: 10.1109/TSTE.2018.2831704.

[21] N. Mohan and T. M. Undeland: Power electronics: converters, applications, and design. John Wiley & Sons, 2007.

[22] M. Badoni, et al.: Grid interfaced solar photovoltaic system using ZA-LMS based control algorithm. Electric Power Systems Research, 160, (2018), 261–272, DOI: 10.1016/j.epsr.2018.03.001.

[23] M. Rezkallah, et al.: Lyapunov function and sliding mode control approach for the solar-PV grid interface system. IEEE Transactions on Industrial Electronics, 64(1), (2016), 785–795, DOI: 10.1109/tie.2016.2607162.

[24] N. Kumar, B. Singh, and B.K. Panigrahi: Integration of Solar PV with Low- Voltage Weak Grid System: using Maximize-M Kalman Filter and Self-Tuned P&O Algorithm. IEEE Transactions on Industrial Electronics, 66(11), (2019), 9013–9022, DOI: 10.1109/tie.2018.2889617.

[25] H. Sharma, G. Hazrati, and J.Ch.Bansal: Spider monkey optimization algorithm. Evolutionary and swarm intelligence algorithms. Springer, Cham, 2019, 43–59.

[26] K. Neelu, P. Devan, Ch.L. Chowdhary, S. Bhattacharya, G. Singh, S. Singh, and B. Yoon: Smo-dnn: Spider monkey optimization and deep neural network hybrid classifier model for intrusion detection. Electronics, 9(4), (2020), 692, DOI: 10.3390/electronics9040692.

[27] M.A.H. Akhand, S.I. Ayon, A.A. Shahriyar, and N. Siddique: Discrete spider monkey optimization for travelling salesman problem. Applied Soft Computing, 86 (2020), DOI: 10.1016/j.asoc.2019.105887.

[28] Avinash Sharma, Akshay Sharma, B.K. Panigrahi, D. Kiran, and R. Kumar: Ageist spider monkey optimization algorithm. Swarm and Evolutionary Computation, 28 (2016), 58–77, DOI: 10.1016/j.swevo.2016.01.002.

[29] Sriram Mounika and K. Ravindra: Backtracking Search Optimization Algorithm Based MPPT Technique for Solar PV System. In Advances in Decision Sciences, Image Processing, Security and Computer Vision. Springer, Cham, 2020, 498–506.

[30] Pilakkat, Deepthi and S. Kanthalakshmi: Single phase PV system operating under Partially Shaded Conditions with ABC-PO as MPPT algorithm for grid connected applications. Energy Reports, 6 (2020), 1910–1921, DOI: 10.1016/j.egyr.2020.07.019.

[31] R. Gessing: Controllers of the boost DC-DC converter accounting its minimum- and non-minimum-phase nature. Archives of Control Sciences, 19(3), (2009), 245–259.

[32] A. Talha and H. Boumaaraf: Evaluation of maximum power point tracking methods for photovoltaic systems. Archives of Control Sciences, 21(2), (2011), 151–165.

[33] S.N. Singh and S. Mishra: FPGA implementation of DPWM utility/DG interfaced solar (PV) power converter for green home power supply. Archives of Control Sciences, 21(4), (2011), 461–469.

Go to article
[2] S. Gulkowski, J.V.M. Diez, J.A. Tejero, and G. Nofuentes: Computational modeling and experimental analysis of heterojunction with intrinsic thin-layer photovoltaic module under different environmental conditions. Energy, 172, (2019), 380–390, DOI: 10.1016/j.energy.2019.01.107.

[3] M. Bahrami, et al.: Hybrid maximum power point tracking algorithm with improved dynamic performance. Renewable Energy, 130, (2019), 982–991, DOI: 10.1016/j.renene.2018.07.020.

[4] K.V. Singh, Krishna, H. Bansal, and D. Singh: A comprehensive review on hybrid electric vehicles: architectures and components. Journal of Modern Transportation, 27, (2019), 1–31, DOI: 10.1007/s40534-019-0184-3.

[5] S. Pradhan, et al.: Performance Improvement of Grid-Integrated Solar PV System Using DNLMS Control Algorithm. IEEE Transactions on Industry Applications, 55(1), (2019), 78–91, DOI: 10.1109/TIA.2018.2863652.

[6] S. Negari and D. Xu: Utilizing a Lagrangian approach to compute maximum fault current in hybrid AC–DC distribution grids withMMCinterface. High Voltage, 4(1), (2019), 18–27, DOI: 10.1049/hve.2018.5087.

[7] V.T. Tran et al.: Mitigation of Solar PV Intermittency Using Ramp-Rate Control of Energy Buffer Unit. IEEE Transactions on Energy Conversion, 34(1), (2019), 435–445, DOI: 10.1109/TEC.2018.2875701.

[8] A. Kihal, et al.: An improved MPPT scheme employing adaptive integral derivative sliding mode control for photovoltaic systems under fast irradiation changes. ISA Transactions, 87, (2019), 297–306, DOI: 10.1016/j.isatra.2018.11.020.

[9] A.M. Jadhav, N.R. Patne, and J.M. Guerrero: A novel approach to neighborhood fair energy trading in a distribution network of multiple microgrid clusters. IEEE Transactions on Industrial Electronics, 66(2), (2019), 1520– 1531, DOI: 10.1109/TIE.2018.2815945.

[10] A. Fragaki, T. Markvart, and G. Laskos: All UK electricity supplied by wind and photovoltaics – The 30–30 rule. Energy, 169, (2019), 228–237, DOI: 10.1016/j.energy.2018.11.151.

[11] S.Z. Ahmed, et al.: Power quality enhancement by using D-FACTS systems applied to distributed generation. International Journal of Power Electronics and Drive Systems, 10(1), (2019), 330, DOI: 10.11591/ijpeds.v10.i1.pp330-341.

[12] H.H. Alhelou, et al.: A Survey on Power System Blackout and Cascading Events: Research Motivations and Challenges. Energies. 12(4), (2019), 1– 28, DOI: 10.3390/en12040682.

[13] M. Badoni, A. Singh, and B. Singh: Implementation of Immune Feedback Control Algorithm for Distribution Static Compensator. IEEE Transactions on Industry Applications, 55(1), (2019), 918–927, DOI: 10.1109/TIA.2018.2867328.

[14] S.R. Das, et al.: Performance evaluation of multilevel inverter based hybrid active filter using soft computing techniques. Evolutionary Intelligence (2019), 1–11, DOI: 10.1007/s12065-019-00217-6.

[15] F. Chishti, S. Murshid, and B. Singh: LMMN Based Adaptive Control for Power Quality Improvement of Grid Intertie Wind-PV System. IEEE Transactions on Industrial Informatics, 15(9), (2019), 4900–4912, DOI: 10.1109/TII.2019.2897165.

[16] S. Pradhan, et al.: Performance Improvement of Grid-Integrated Solar PV System Using DNLMS Control Algorithm. IEEE Transactions on Industry Applications, 55(1), (2019), 78–91, DOI: 10.1109/IICPE.2016.8079455.

[17] V. Jain, I. Hussain, and B. Singh: A HTF-Based Higher-Order Adaptive Control of Single-Stage Grid-Interfaced PV System. IEEE Transactions on Industry Applications, 55(2), (2019), 1873–1881, DOI: 10.1109/TIA.2018.2878186.

[18] N. Kumar, B. Singh, B. Ketan Panigrahi and L. Xu: Leaky Least Logarithmic Absolute Difference Based Control Algorithm and Learning Based InC MPPT Technique for Grid Integrated PV System. IEEE Transactions on Industrial Electronics. 66(11), (2019), 9003–9012, DOI: 10.1109/TIE.2018.2890497.

[19] P. Shah, I. Hussain, and B. Singh: Single-Stage SECS Interfaced with Grid Using ISOGI-FLL- Based Control Algorithm. IEEE Transactions on Industry Applications, 55(1), (2019), 701–711, DOI: 10.1109/TIA.2018.2869880.

[20] V. Jain and B. Singh: A Multiple Improved Notch Filter-Based Control for a Single-StagePVSystem Tied to aWeak Grid. IEEE Transactions on Sustainable Energy, 10(1), (2019), 238–247, DOI: 10.1109/TSTE.2018.2831704.

[21] N. Mohan and T. M. Undeland: Power electronics: converters, applications, and design. John Wiley & Sons, 2007.

[22] M. Badoni, et al.: Grid interfaced solar photovoltaic system using ZA-LMS based control algorithm. Electric Power Systems Research, 160, (2018), 261–272, DOI: 10.1016/j.epsr.2018.03.001.

[23] M. Rezkallah, et al.: Lyapunov function and sliding mode control approach for the solar-PV grid interface system. IEEE Transactions on Industrial Electronics, 64(1), (2016), 785–795, DOI: 10.1109/tie.2016.2607162.

[24] N. Kumar, B. Singh, and B.K. Panigrahi: Integration of Solar PV with Low- Voltage Weak Grid System: using Maximize-M Kalman Filter and Self-Tuned P&O Algorithm. IEEE Transactions on Industrial Electronics, 66(11), (2019), 9013–9022, DOI: 10.1109/tie.2018.2889617.

[25] H. Sharma, G. Hazrati, and J.Ch.Bansal: Spider monkey optimization algorithm. Evolutionary and swarm intelligence algorithms. Springer, Cham, 2019, 43–59.

[26] K. Neelu, P. Devan, Ch.L. Chowdhary, S. Bhattacharya, G. Singh, S. Singh, and B. Yoon: Smo-dnn: Spider monkey optimization and deep neural network hybrid classifier model for intrusion detection. Electronics, 9(4), (2020), 692, DOI: 10.3390/electronics9040692.

[27] M.A.H. Akhand, S.I. Ayon, A.A. Shahriyar, and N. Siddique: Discrete spider monkey optimization for travelling salesman problem. Applied Soft Computing, 86 (2020), DOI: 10.1016/j.asoc.2019.105887.

[28] Avinash Sharma, Akshay Sharma, B.K. Panigrahi, D. Kiran, and R. Kumar: Ageist spider monkey optimization algorithm. Swarm and Evolutionary Computation, 28 (2016), 58–77, DOI: 10.1016/j.swevo.2016.01.002.

[29] Sriram Mounika and K. Ravindra: Backtracking Search Optimization Algorithm Based MPPT Technique for Solar PV System. In Advances in Decision Sciences, Image Processing, Security and Computer Vision. Springer, Cham, 2020, 498–506.

[30] Pilakkat, Deepthi and S. Kanthalakshmi: Single phase PV system operating under Partially Shaded Conditions with ABC-PO as MPPT algorithm for grid connected applications. Energy Reports, 6 (2020), 1910–1921, DOI: 10.1016/j.egyr.2020.07.019.

[31] R. Gessing: Controllers of the boost DC-DC converter accounting its minimum- and non-minimum-phase nature. Archives of Control Sciences, 19(3), (2009), 245–259.

[32] A. Talha and H. Boumaaraf: Evaluation of maximum power point tracking methods for photovoltaic systems. Archives of Control Sciences, 21(2), (2011), 151–165.

[33] S.N. Singh and S. Mishra: FPGA implementation of DPWM utility/DG interfaced solar (PV) power converter for green home power supply. Archives of Control Sciences, 21(4), (2011), 461–469.

11
Dynamics, control, stability, diffusion and synchronization of modified chaotic Colpitts oscillator

The purpose of this paper is to introduce a new chaotic oscillator. Although different chaotic systems have been formulated by earlier researchers, only a few chaotic systems exhibit chaotic behaviour. In this work, a new chaotic system with chaotic attractor is introduced. It is worth noting that this striking phenomenon rarely occurs in respect of chaotic systems. The system proposed in this paper has been realized with numerical simulation. The results emanating from the numerical simulation indicate the feasibility of the proposed chaotic system. More over, chaos control, stability, diffusion and synchronization of such a system have been dealt with.

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[6] A. Cenys, A. Tamasevicius, A.Baziliauskas, R. Krivickas, and E. Lind- berg: Hyperchaos in coupled Colpitts oscillators. Chaos, Solitons & Fractals, 17 (2003), DOI: 10.1016/S0960-0779(02)00373-9.

[7] C.M. Kim, S. Rim, W.H. Kye, J.W. Ryu, and Y.J. Park: Anti-synchronization of chaotic oscillators. Physics Letters A, 320 (2003), 39–46, DOI: 10.1016/j.physleta.2003.10.051.

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[9] S. Vaidyanathan, A. Sambas, and S. Zhang: A new 4-D dynamical system exhibiting chaos with a line of rest points, its synchronization and circuit model. Archives of Control Sciences, 29 (2019), DOI: 10.24425/acs.2019.130202.

[10] C.K. Volos, V.T. Pham, S. Vaidyanathan, I.M. Kyprianidis, and I.N. Stouboulos: Synchronization phenomena in coupled Colpitts circuits. Journal of Engineering Science & Technology Review, 8 (2015).

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[13] J.Y. Effa, B.Z. Essimbi, and J.M. Ngundam: Synchronization of improved chaotic Colpitts oscillators using nonlinear feedback control. Nonlinear Dynamics, 58 (2009), 39–47, DOI: 10.1007/s11071-008-9459-7.

[14] S. Mishra, A.K. Singh, and R.D.S. Yadava: Effects of nonlinear capacitance in feedback LC-tank on chaotic Colpitts oscillator. Physica Scripta, 95 (2020), 055203. DOI: 10.1088/1402-4896/ab6f95.

[15] S. Vaidyanathan and S. Rasappan: Global chaos synchronization of nscroll Chua circuit and Lur’e system using backstepping control design with recursive feedback. Arabian Journal for Science and Engineering, 39 (2014), 3351–3364, DOI: 10.1007/s13369-013-0929-y.

[16] R. Suresh and V. Sundarapandian: Hybrid synchronization of nscroll Chua and Lur’e chaotic systems via backstepping control with novel feedback. Archives of Control Sciences, 22 (2012), 343–365, DOI: 10.2478/v10170-011-0028-9.

[17] S. Rasappan: Synchronization of neuronal bursting using backstepping control with recursive feedback. Archives of Control Sciences, 29 (2019), 617–642, DOI: 10.24425/acs.2019.131229.

[18] H.B. Fotsin and J.Daafouz:Adaptive synchronization of uncertain chaotic Colpitts oscillators based on parameter identification. Physics Letters A, 339 (2005), 304–315, DOI: 10.1016/j.physleta.2005.03.049.

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Go to article
[2] S. Vaidyanathan, K. Rajagopal, C.K. Volos, I.M. Kyprianidis, and I.N. Stouboulos: Analysis, adaptive control and synchronization of a seventerm novel 3-D chaotic system with three quadratic nonlinearities and its digital implementation in labview. Journal of Engineering Science and Technology Review, 8 (2015), 130–141.

[3] P. Kvarda: Identifying the deterministic chaos by using the Lyapunov exponents. Radioengineering-Prague, 10 (2001), 38–38.

[4] Y.C. Lai and C. Grebogi: Modeling of coupled chaotic oscillators. Physical Review Letters, 82 (1999), 4803, DOI: 10.1103/PhysRevLett.82.4803.

[5] H. Deng and D. Wang: Circuit simulation and physical implementation for a memristor-based Colpitts oscillator. AIP Advances, 7 (2017), 035118, DOI: 10.1063/1.4979175.

[6] A. Cenys, A. Tamasevicius, A.Baziliauskas, R. Krivickas, and E. Lind- berg: Hyperchaos in coupled Colpitts oscillators. Chaos, Solitons & Fractals, 17 (2003), DOI: 10.1016/S0960-0779(02)00373-9.

[7] C.M. Kim, S. Rim, W.H. Kye, J.W. Ryu, and Y.J. Park: Anti-synchronization of chaotic oscillators. Physics Letters A, 320 (2003), 39–46, DOI: 10.1016/j.physleta.2003.10.051.

[8] A.S. Elwakil and M.P. Kennedy: A family of Colpitts-like chaotic oscillators. Journal of the Franklin Institute, 336 (1999), 687–700, DOI: 10.1016/S0016-0032(98)00046-5.

[9] S. Vaidyanathan, A. Sambas, and S. Zhang: A new 4-D dynamical system exhibiting chaos with a line of rest points, its synchronization and circuit model. Archives of Control Sciences, 29 (2019), DOI: 10.24425/acs.2019.130202.

[10] C.K. Volos, V.T. Pham, S. Vaidyanathan, I.M. Kyprianidis, and I.N. Stouboulos: Synchronization phenomena in coupled Colpitts circuits. Journal of Engineering Science & Technology Review, 8 (2015).

[11] H. Fujisaka and T. Yamada: Stability theory of synchronized motion in coupled-oscillator systems. Progress of theoretical physics, 69 (1983), 32– 47, DOI: 10.1143/PTP.69.32.

[12] N.J. Corron, S.D. Pethel, and B.A. Hopper: Controlling chaos with simple limiters. Physical Review Letters, 84 (2000), 3835, DOI: 10.1103/Phys-RevLett.84.3835.

[13] J.Y. Effa, B.Z. Essimbi, and J.M. Ngundam: Synchronization of improved chaotic Colpitts oscillators using nonlinear feedback control. Nonlinear Dynamics, 58 (2009), 39–47, DOI: 10.1007/s11071-008-9459-7.

[14] S. Mishra, A.K. Singh, and R.D.S. Yadava: Effects of nonlinear capacitance in feedback LC-tank on chaotic Colpitts oscillator. Physica Scripta, 95 (2020), 055203. DOI: 10.1088/1402-4896/ab6f95.

[15] S. Vaidyanathan and S. Rasappan: Global chaos synchronization of nscroll Chua circuit and Lur’e system using backstepping control design with recursive feedback. Arabian Journal for Science and Engineering, 39 (2014), 3351–3364, DOI: 10.1007/s13369-013-0929-y.

[16] R. Suresh and V. Sundarapandian: Hybrid synchronization of nscroll Chua and Lur’e chaotic systems via backstepping control with novel feedback. Archives of Control Sciences, 22 (2012), 343–365, DOI: 10.2478/v10170-011-0028-9.

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[18] H.B. Fotsin and J.Daafouz:Adaptive synchronization of uncertain chaotic Colpitts oscillators based on parameter identification. Physics Letters A, 339 (2005), 304–315, DOI: 10.1016/j.physleta.2005.03.049.

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