Title: Simple adaptive control strategy for a class of systems subjected to real parametric uncertainty with application to unified chaotic system

Authors: Ishan Garg; Bharat Bhushan Sharma

Addresses: Electrical Engineering Department, National Institute of Technology Hamirpur (HP), 177005, India ' Electrical Engineering Department, National Institute of Technology Hamirpur (HP), 177005, India

Abstract: In this paper, a relatively simplified adaptive control strategy for set of chaotic systems is presented. The results utilise the basic linear state feedback control strategy blended with algebraic matrix Riccati equation (AMRE) to derive the control mechanism for chaotic systems operating in uncertain environment. The proposed approach utilises lesser number of control inputs in comparison to methods available in literature. Moreover, the controller structure turns out to be simple linear combination of states of system for the chaotic systems belonging to the proposed class, which are otherwise handled with nonlinear controller design strategies. The Lyapunov stability approach is exploited to analytically derive the control function and the parametric updation laws for uncertain parameters. Extensive simulation results are elaborated for set of chaotic systems to demonstrate effectiveness and validity of the presented approach.

Keywords: chaotic systems; linear adaptive controller; Lyapunov stability theory; parametric uncertainty; algebraic matrix Riccati equation; AMRE.

DOI: 10.1504/IJNDC.2021.117085

International Journal of Nonlinear Dynamics and Control, 2021 Vol.2 No.1, pp.33 - 50

Received: 23 Jun 2020
Accepted: 24 Nov 2020
Published online: 16 Aug 2021 *

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