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.
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