An adaptive feedback controller with observer for linearizable chaotic systems

Authors:
A. Boulkroune;M. Chekireb;M. Tadjine;S. Bouatmane
Affiliations:
University of Jijel, Jijel, Algeria;ENP, Algiers, Algeria;ENP, Algiers, Algeria;University of Jijel, Jijel, Algeria
Venue:
Control and Intelligent Systems
Year:
2007

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Abstract

In this paper, an adaptive feedback controller with observer is developed for a class of chaotic systems. This controller does not need the availability of state variables. It can be used for tracking a smooth orbit that can be a limit cycle or a chaotic orbit of another system. This adaptive feedback controller is constructed with H∞ control technique. Based on Lyapunov stability theorem, the proposed adaptive feedback control system can guarantee the stability of whole closed-loop system and achieve the H∞ tracking performance as well. To demonstrate the efficiency of the proposed scheme, two well-known chaotic systems namely Duffing-Holmes system and Lur'e-like system are considered as illustrative examples.