Observer-Based Adaptive Feedback Controller of a Class of Chaotic Systems

In this paper, an observer-based adaptive feedback controller 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 the aid of its H ∞ control technique to achieve the H ∞ tracking performance. Based on Lyapunov stability theorem, the proposed adaptive feedback control system can guarantee the stability of whole closed-loop system and obtain good tracking performance as well. To demonstrate the efficiency of the proposed scheme, two well-known chaotic systems, namely Chua's circuit and Lur'e system are considered as illustrative examples.