### Details

#### Title

Heating control of a finite rod with a mobile source#### Journal title

Archives of Control Sciences#### Yearbook

2021#### Volume

vol. 31#### Issue

No 2#### Affiliation

Jilavyan, Samvel H. : Faculty of Mathematics and Mechanics, Yerevan State University, 1 Alex Manoogian, 0025 Yerevan, Armenia ; Grigoryan, Edmon R. : Faculty of Mathematics and Mechanics, Yerevan State University, 1 Alex Manoogian, 0025 Yerevan, Armenia ; Khurshudyan, Asatur Zh. : Dynamicsof Deformable Systems and Coupled Fields, Institute of Mechanics, National Academy of Sciences of Armenia, 0019 Yerevan, Armenia#### Authors

#### Keywords

null-controllability ; mobile control ; nonlinear constraints ; triangular wave ; rectangular wave ; Green’s function approach ; heuristic control ; lack of exact controllability#### Divisions of PAS

Nauki Techniczne#### Coverage

417-430#### Publisher

Committee of Automatic Control and Robotics PAS#### Bibliography

[1] J. Klamka:*Controllability of Dynamical Systems*. Kluwer Academic, Dordrecht, 1991.

[2] S.A. Avdonin and S.A. Ivanov:

*Families of Exponentials. The Method of Moments in Controllability Problems for Distributed Parameter Systems*. Cambridge University Press, New York, 1995.

[3] A. Fursikov and O.Yu. Imanuvilov:

*Controllability of Evolution Equations*. Lecture Notes Series, vol. 34. Seoul National University, Research Institute of Mathematics, Global Analysis Research Center, Seoul, 1996.

[4] E. Zuazua:

*Controllability and Observability of Partial Differential Equations: Some Results and Open Problems*. Handbook of Differential Equations: Evolutionary Differential Equations, vol. 3, Elsevier/North-Holland, Amsterdam, 2006.

[5] R. Glowinski, J.-L. Lions and J. He:

*Exact and Approximate Controllability for Distributed Parameter Systems: A Numerical Approach*. Cambridge University Press, New York, 2008.

[6] A.S. Avetisyan and As.Zh. Khurshudyan:

*Controllability of Dynamic Systems: The Green’s Function Approach*. Cambridge Scholars Publishing, Cambridge, 2018.

[7] S. Micu and E. Zuazua: On the lack of null-controllability of the heat equation on the half-line.

*Transactions of the American Mathematical Society*, 353(4), (2001), 1635–1659.

[8] S. Micu and E. Zuazua:

*Null Controllability of the Heat Equation in Unbounded Domains*. In “Unsolved Problems in Mathematical Systems and Control Theory”, edited by Blondel V.D., Megretski A., Princeton University Press, Princeton, 2004.

[9] V. Barbu: Exact null internal controllability for the heat equation on unbounded convex domain.

*ESAIM: Control, Optimisation and Calculus of Variations*, 20 (2014), 222–235, DOI: 10.1051/cocv/2013062.

[10] As.Zh. Khurshudyan: (2019), Distributed controllability of heat equation in un-bounded domains: The Green’s function approach.

*Archives of Control Sciences*, 29(1), (2019), 57–71, DOI: 10.24425/acs.2019.127523.

[11] S. Ivanov and L. Pandolfi: Heat equation with memory: Lack of controllability to rest.

*Journal of Mathematical Analysis and Applications*, 355 (2009), 1–11, DOI: 10.1016/j.jmaa.2009.01.008.

[12] A. Halanay and L. Pandolfi: Approximate controllability and lack of controllability to zero of the heat equation with memory.

*Journal of Mathematical Analysis and Applications,*425 (2015), 194–211, DOI: 10.1016/j.jmaa.2014.12.021.

[13] B.S. Yilbas:

*Laser Heating Applications: Analytical Modelling*. Elsevier, Waltham, 2012.

[14] A.G. Butkovskiy and L.M. Pustylnikov:

*Mobile Control of Distributed Parameter Systems*. Chichester, Ellis Horwood, 1987.

[15] V.A. Kubyshkin and V.I. Finyagina:

*Moving control of systems with distributed parameters*(in Russian). Moscow: SINTEG, 2005.

[16] Sh.Kh. Arakelyan and As.Zh. Khurshudyan: The Bubnov-Galerkin procedure for solving mobile control problems for systems with distributed parameters. Mechanics.

*PNAS Armenia*, 68(3), (2015), 54–75.

[17] A.G. Butkovskiy: Some problems of control of the distributed-parameter systems.

*Automation and Remote Control*, 72 (2011), 1237–1241, DOI: 10.1134/S0005117911060105.

[18] A.S. Avetisyan and As.Zh. Khurshudyan: Green’s function approach in approximate controllability problems.

*Proceedings of National Academy of Sciences of Armenia. Mechanics*, vol. 69, issue 2, (2016), 3–22, DOI: 10.33018/69.2.1.

[19] A.S. Avetisyan and As.Zh. Khurshudyan: Green’s function approach in approximate controllability of nonlinear physical processes.

*Modern Physics Letters A*, 32 1730015, (2017), DOI: 10.1142/S0217732317300154.

[20] As.Zh. Khurshudyan: Resolving controls for the exact and approximate controllabilities of the viscous Burgers’ equation: the Green’s function approach.

*International Journal of Modern Physics C,*29(6), 1850045, (2018), DOI: 10.1142/S0129183118500456.

[21] A.S. Avetisyan and As.Zh. Khurshudyan: Exact and approximate controllability of nonlinear dynamic systems in infinite time: The Green’s function approach.

*ZAMM*, 98(11), (2018), 1992–2009, DOI: 10.1002/zamm.201800122.

[22] As.Zh. Khurshudyan: Exact and approximate controllability conditions for the micro-swimmers deflection governed by electric field on a plane: The Green’s function approach.

*Archives of Control Sciences*, 28(3), (2018), 335–347. DOI: 10.24425/acs.2018.124706.

[23] J. Klamka and As.Zh. Khurshudyan: Averaged controllability of heat equation in unbounded domains with uncertain geometry and location of controls: The Green’s function approach. Archives of Control Sciences, 29(4), (2019), 573–584, DOI: 10.24425/acs.2018.124706.

[24] J. Klamka, A.S. Avetisyan and As.Zh. Khurshudyan: Exact and approximate distributed controllability of the KdV and Boussinesq equations: The Green’s function approach. Archives of Control Sciences, 30(1), (2020), 177–193, DOI: 10.24425/acs.2020.132591.

[25] J. Klamka and As.Zh. Khurshudyan: Approximate controllability of second order infinite dimensional systems. Archives of Control Sciences, 31(1), (2021), 165–184, DOI: 10.24425/acs.2021.136885.

[26] As.Zh. Khurshudyan: Heuristic determination of resolving controls for exact and approximate controllability of nonlinear dynamic systems. Mathematical Problems in Engineering, (2018), Article ID 9496371, DOI: 10.1155/2018/9496371.

[27] H. Hossain and As.Zh. Khurshudyan: Heuristic control of nonlinear power systems: Application to the infinite bus problem. Archives of Control Sciences, 29(2), (2019), 279–288, DOI: 10.24425/acs.2019.129382. [28] A.G. Butkovskii and L.M. Pustyl’nikov: Characteristics of Distributed- Parameter Systems. Kluwer Academic Publishers, 1993.