Thursday , January 23 2020

An Enhanced Stabilizing Strategy for Switched Nonlinear Systems*

Faiçal HAMIDI1, Houssem JERBI2*, Severus Constantin OLTEANU3, Dumitru POPESCU3
University of Gabès, Laboratory “Modelisation, Analyse et Commande des Systemes”, LR16ES22, Gabès, Tunisia
faical.hmidi@isimg.tn
2 University of Ha’il, College of Engineering – Department of Industrial Engineering KSA
h.jerbi@uoh.edu.sa (*Corresponding author)
University Politehnica of Bucharest, Faculty of Automatic Control and Computer Science, Bucharest, Romania
dumitru.popescu@acse.pub.ro

Abstract: This study examines a computational technique used to design a novel feedback control law based on an expansion strategy of the Attraction Domain (DA) for a class of nonlinear switched systems. It is supposed that the state space is distributed into numerous regions without any intersections and modelled by polynomial inequalities. The main concept involves the maximization of the DA for local subsystems surrounding particular operational points. It was demonstrated that the DA can be ascertained by joining a Genetic Algorithmic method (GA) as an enhanced optimisation approach with the LMI method for a specified Lyapunov function. The feedback controller can then be constructed in order to ensure a global stability by using the Multiple Lyapunov function sets via switching signals. The effectiveness of this evolved strategy is eventually confirmed via a simulation examination by means of the benchmark Van der Pol oscillator.

Keywords: Nonlinear switched models, Multiple Lyapunov function, Stability, LMI, Genetic Algorithms, Domain of Attraction (DA).

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CITE THIS PAPER AS:
Faiçal HAMIDI, Houssem JERBI, Severus Constantin OLTEANU, Dumitru POPESCUAn Enhanced Stabilizing Strategy for Switched Nonlinear System, Studies in Informatics and Control, ISSN 1220-1766, vol. 28(4), pp. 391-400, 2019. https://doi.org/10.24846/v28i4y201903

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* This paper is an extended version of the paper called “Enlarging the Domain of Attraction in Nonlinear Polynomial Systems”, published in the International Journal of Computers Communications and Control, 8(4), 538-547. In the current paper, a feedback controller has been constructed to ensure a global stability for a class of hybrid systems by using the multiple Lyapunov function sets via switching signals. The control strategy is detailed and a synthesized algorithm is recommended. The effectiveness of this evolved strategy is eventually confirmed via a simulation examination. A numerical simulation analysis is carried out proving the satisfactory performances of the developed control scheme.