2020 (vol. 30) - Number 4

*A.B. Malinowska, R. Kamocki, R. Almeida, T. Odzijewicz:*

On the existence of optimal consensus control for the fractional Cucker--Smale model

*R. Grymin, W. Bożejko, J. Pempera, M. Wodecki, Z. Chaczko:*

Algorithm for solving the Discrete-Continuous Inspection Problem

*T. Kaczorek, A. Ruszewski:*

Global stability of discrete-time nonlinear systems with descriptor standard and fractional positive linear parts and scalar feedbacks

*R. Arora, K. Gupta:*

Fuzzy goal programming technique for multi-objective indefinite quadratic bilevel programming problem

*P. Nowak, J. Czeczot, P. Grelewicz:*

Tuning rules for industrial use of the second-order Reduced Active Disturbance Rejection Controller

*M.I. Gomoyunov:*

Optimal control problems with a fixed terminal time in linear fractional-order systems

*Muhafzan, A. Nazra, L. Yulianti, Zulakmal, R. Revina:*

On LQ optimization problem subject to fractional order irregular singular systems

*M. Blizorukova, V. Maksimov:*

On one algorithm for reconstruction of an disturbance in a linear system of ordinary differential equations

ACS Abstract:

**2019 (Volume 29)**

Number 2

Cellular particle swarm optimization with a simple adaptive local search strategy for the permutation flow shop scheduling problem

J. Seck-Tuoh-Mora, J. Medina-Marin, E.S. Martinez-Gomez, E.S. Hernandez-Gress, N. Hernandez-Romero, V. Volpi-Leon(Autonomous University of Hidalgo State, Mexico) |

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.

**keywords:** flow shop, particle swarm optimization, local search strategy, hybrid search method, cellular automata, scheduling

A separation principle for Takagi-Sugeno control fuzzy systems

N. Hadj Taieb, M.A. Hammami( University of Sfax, Tunisia) | F. Delmotte(University of Artois, France) |

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 illustrate the applicability of the main result.

**keywords:** T-S model, PDC controller, fuzzy observer, separation principle

Absolute stability of a class of nonlinear systems with nonpositive linear parts

Tadeusz Kaczorek(Bialystok University of Technology, Poland) |

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.

**keywords:** absolute stability, positive, nonlinear, discrete-time, continuous-time, systems

Global rational stabilization of a class of nonlinear time-delay systems

Nadhem Echi, Boulbaba Ghanmi(Gafsa University, Tunisia) |

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.

**keywords:** rational stability, delay system, nonlinear observer, Lyapunov functional

Heuristic control of nonlinear power systems: Application to the infinite bus problem

Md Musabbir Hossain(Shanghai University, China) | Asatur Zh. Khurshudyan(NAS of Armenia and Shanghai Jiao Tong University, China) |

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.

**keywords:** power systems, nonlinear control, heuristic method, harmonic control, piecewise constant control

Interval state estimation for linear time-varying (LTV) discrete-time systems subject to component faults and uncertainties

Awais Khan, Wei Xie, Langwen Zhang, Ihsanullah(South China University of Technology, China) |

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 LTV discrete-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.

**keywords:** component faults, interval state estimator, linear time-varying systems, non-cooperative systems

Synchronization of fractional order Rabinovich-Fabrikant systems using sliding mode control techniques

Sanjay Kumar, Chaman Singh, Sada Nand Prasad, Chandra Shekhar, Rajiv Aggarwal(University of Delhi, India) |

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 analyzed 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.

**keywords:** fractional-order chaotic system, chaos synchronization, Rabinovich-Fabrikant system, Lyapunov exponents

Numerical error bound of optimal control for homogeneous linear systems

Adnan Daraghmeh, Naji Qatanani(An-Najah National University, Palestine) |

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.

**keywords:** time-invariant systems, quadratic cost function, linear quadratic regulator, agebraic Riccati equation, Hamiltonian function, L_2 norm

Dual hesitant Pythagorean fuzzy Bonferroni mean operators in multi-attribute decision making

Xiyue Tang, Guiwu Wei(Sichuan Normal University, China) |

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.

**keywords:** 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 c

Tracking control for a cascade perturbed control system using the active disturbance rejection paradigm

R. Patelski, D. Pazderski(Poznan University of Technology, Poland) |

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.

**keywords:** active disturbance rejection, cascade control systems, stability of perturbed systems, high-precision tracking control, control of astronomical mounts

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