Słowa kluczowe:
flow shop
particle swarm optimization
local search strategy
hybrid search method
cellular automata
scheduling

Permutation flow shop scheduling problem deals with the production planning of a number of jobs processed by a set of machines in the same order. Several metaheuristics have been proposed for minimizing the makespan of this problem. Taking as basis the previous Alternate Two-Phase PSO (ATPPSO) method and the neighborhood concepts of the Cellular PSO algorithm proposed for continuous problems, this paper proposes the improvement of ATPPSO with a simple adaptive local search strategy (called CAPSO-SALS) to enhance its performance. CAPSO-SALS keeps the simplicity of ATPPSO and boosts the local search based on a neighborhood for every solution. Neighbors are produced by interchanges or insertions of jobs which are selected by a linear roulette scheme depending of the makespan of the best personal positions. The performance of CAPSO-SALS is evaluated using the 12 different sets of Taillard’s benchmark problems and then is contrasted with the original and another previous enhancement of the ATPPSO algorithm. Finally, CAPSO-SALS is compared as well with other ten classic and state-of-art metaheuristics, obtaining satisfactory results.

Słowa kluczowe:
T-S model
PDC controller
fuzzy observer
separation principle

An important application of state estimation is feedback control: an estimate of the state (typically the mean estimate) is used as input to a state-feedback controller. This scheme is known as observer based control, and it is a common way of designing an output-feedback controller (i.e. a controller that does not have access to perfect state measurements). In this paper, under the fact that both the estimator dynamics and the state feedback dynamics are stable we propose a separation principle for Takagi-Sugeno fuzzy control systems with Lipschitz nonlinearities. The considered nonlinearities are Lipschitz or meets an integrability condition which have no influence on the LMI to prove the stability of the associated closed-loop system. Furthermore, we give an example to ullistrate the applicability of the main result.

Słowa kluczowe:
absolute stability
positive
nonlinear
discrete-time
continuous-time
systems

The positivity and absolute stability of a class of nonlinear continuous-time and discrete-time systems with nonpositive linear part are addressed. Necessary and sufficient conditions for the positivity of this class of nonlinear systems are established. Sufficient conditions for the absolute stability of this class of nonlinear systems are also given.

Słowa kluczowe:
rational stability
delay system
nonlinear observer
Lyapunov functional

The present paper is mainly aimed at introducing a novel notion of stability of nonlinear time-delay systems called Rational Stability. According to the Lyapunov-type, various sufficient conditions for rational stability are reached. Under delay dependent conditions, we suggest a nonlinear time-delay observer to estimate the system states, a state feedback controller and the observer-based controller rational stability is provided. Moreover, global rational stability using output feedback is given. Finally, the study presents simulation findings to show the feasibility of the suggested strategy.

Słowa kluczowe:
power systems
nonlinear control
heuristic method
harmonic control
piece-wise constant control

In this paper, we apply the heuristic method for determination of control functions for controllability analysis of nonlinear power systems. The problem of control of quasi-linear systems under proper assumptions on the nonlinear term is considered in the general statement. Making use of the Green’s function solution of nonlinear systems, the exact and approximate controllability conditions are expressed in terms of unknown controls in an explicit form. The way of resolving controls determination is discussed. As a particular application, a one-machine infinite-bus system is considered described by a coupled system of three first order ordinary differential equations. Two heuristic forms of admissible controls are considered providing approximate controllability within the same amount of time having different intensities. Results of numerical simulations are presented and discussed.

Słowa kluczowe:
component faults
interval state estimator
linear time-varying systems
non-cooperative systems

This paper deals with the design of an interval state estimator for linear time-varying (LTV) discrete-time systems subject to component faults and uncertainties. These component faults and uncertainties are assumed to be unknown but bounded without giving any other information, whose effect can be approximated using these bounds. In the first part of this work, an interval state estimator for such systems is designed to deal with these component faults and uncertainties. The result is then extended to find an interval state estimator for a non-cooperative LTVdiscrete-time system subject to component faults and uncertainties by similarity transformation of coordinates. The proposed interval state estimator guaranteed bounds on the observed states that are consistent with the system states. The observer convergence is also ensured. The designed method is simple and easy to be implemented. Two numerical examples are given to show the effectiveness of the proposed method.

Słowa kluczowe:
fractional-order chaotic system
chaos synchronization
Rabinovich-Fabrikant system
Lyapunov exponents

In this research article, we present the concepts of fractional-order dynamical systems and synchronization methodologies of fractional order chaotic dynamical systems using slide mode control techniques. We have analysed the different phase portraits and time-series graphs of fractional order Rabinovich-Fabrikant systems. We have obtained that the lowest dimension of Rabinovich-Fabrikant system is 2.85 through utilization of the fractional calculus and computational simulation. Bifurcation diagrams and Lyapunov exponents of fractional order Rabinovich-Fabrikant system to justify the chaos in the systems. Synchronization of two identical fractional-order chaotic Rabinovich-Fabrikant systems are achieved using sliding mode control methodology.

Słowa kluczowe:
time-invariant systems
quadratic cost function
linear quadratic regulator
algebraic Riccati equation
Hamiltonian function
L2 norm

In this article we focus on the balanced truncation linear quadratic regulator (LQR) with constrained states and inputs. For closed-loop, we want to use the LQR to find an optimal control that minimizes the objective function which called “the quadratic cost function” with respect to the constraints on the states and the control input. In order to do that we have used formal asymptotes for the Pontryagin maximum principle (PMP) and we introduce an approach using the so called *The Hamiltonian Function* and the underlying algebraic Riccati equation. The theoretical results are validated numerically to show that the model order reduction based on open-loop balancing can also give good closed-loop performance.

Słowa kluczowe:
multiple attribute decision making (MADM)
dual hesitant Pythagorean fuzzy sets
dual hesitant Pythagorean fuzzy Bonferroni mean (DHPFBM) operator
dual hesitant Pythagorean fuzzy geometric Bonferroni mean (DHPFGBM) operator
supplier selection
supply chain management

In this paper, we investigate the multiple attribute decision making problems based on the Bonferroni mean operators with dual Pythagorean hesitant fuzzy information. Firstly, we introduce the concept and basic operations of the dual hesitant Pythagorean fuzzy sets, which is a new extension of Pythagorean fuzzy sets. Then, motivated by the idea of Bonferroni mean operators, we have developed some Bonferroni mean aggregation operators for aggregating dual hesitant Pythagorean fuzzy information. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the dual hesitant Pythagorean fuzzy multiple attribute decision making problems. Finally, a practical example for supplier selection in supply chain management is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Słowa kluczowe:
active disturbance rejection
cascade control systems
stability of perturbed systems
high-precision tracking control
control of astronomical mounts

In this paper the stability of a closed-loop cascade control system in the trajectory tracking task is addressed. The considered plant consists of underlying second-order fully actuated perturbed dynamics and the first order system which describes dynamics of the input. The main theoretical result establishes the conditions for Lyapunov stability formulated for the perturbed cascade control structure taking advantage of the active rejection disturbance approach. In particular, limitations imposed on a feasible set of an observer bandwidth are discussed. In order to illustrate characteristics of the closed-loop control system simulation results are presented. Furthermore, the particular implementation of the cascade control algorithm is verified experimentally using a two-axis telescope mount. The obtained results confirm that the considered control strategy can be efficiently applied for a class of mechanical systems when a high position tracking precision is required.

Each paper submitted is subject to a review procedure, and the publication decision is based on reviers' comments on the paper. To avoid delay, please prepare the manuscript carefully following the suggestions listed below.

**Computer file** of the manuscript may be sent by e-mail to the address of Assistant Editor or acs@polsl.pl. Preferred text processors is TeX or LaTeX, however Word and other processors are also acceptable. In case of difficulties in processing the text, the author may be asked to supply the ASCII export of the original file.

**Manuscript**s sent via ordinary post should be typewritten double-spaced on one side of a standard size (A4) paper. Left side margin should be approximately 3cm (1.2'') wide. Each page should contain approximately 30 lines of 60 characters each. The manuscript including figures and tables together with their captions should be submitted. A separate signed letter giving the Author's preferred address for correspondence and return of proofs should be enclosed. Manuscript is the basis for editorial work.

**First page** should include the title of the paper, first name(s) and surname(s) of the Author(s), and a short summary (abstract), not longer than 20 lines.

**Keywords** of max. 5 - 7 items should be included in manuscript.

**Numeration**. All chapters, including the introduction, should be numbered in arabic numerals. Equations, tables and figures as well as theorems, corollaries, examples etc., should be numbered consecutively throughout the paper in arabic numerals, except in appendices. Appendices should be numbered with capital letters, and numeration should be closed within individual appendices.

**If the manuscript is not prepared with TeX**, mathematical expressions should be carefully written so as not to arouse confusion. Care should be taken that subscripts and superscripts are easily readable.

**Tables and figures** should be placed as desired by the Author within the text or on separate sheets with their suggested location indicated by the number of table or figure in the text. Figures, graphs and pictures (referred to as Fig. in the manuscript) should be numbered at the beginning of their caption following the figure. All figures should be prepared as PostScript EPS files or LaTeX picture files; in special cases, bitmaps of figure are also acceptable. The numbers and titles of tables should be placed above the main body of each table.

**References** should be listed alphabetically at the end of the manuscript. They should be numbered in ascending order and the numbers should be inserted in square brackets. References should be organized as follows. First initial(s), surname(s) of the author(s) and title of article or book. Then, for papers: title of periodical or collective work, volume number (year of issue), issue number, and numbers of the first and the last page; for books: publisher's name(s), place and year of issue. Example:

- R. E. Kalman: Mathematical description of linear dynamical system. SIAM J. Control. 1(2), (1963), 152-192.
- F. C. Shweppe: Uncertain dynamic systems. Prentice-Hall, Englewood Cliffs, N.J. 1970.

Please, give full titles of journals; only common words like Journal, Proceedings, Conference, etc. may be abbreviated ( to J., Proc., Conf., ... respectively). References to publications in the body of the manuscript should be indicated by the numbers of the adequate references in square brackets. When the paper is set in TeX the preferable form of preparing references is Bib TeX bib database.

**Footnotes** should be placed in the manuscript, beginning with "Received..." (date to be filled in by Editor), the author's institutional affiliation and acknowledgement of financial support,