Chaotic Control Using Fuzzy Model-Based Methods

In this paper, we propose a fuzzy tracking control for chaotic systems with immeasurable states. First we represent the chaotic and reference systems into T–S fuzzy models. Some properties concerning the premise variable selection and controller placement for chaotic systems are discussed. When considering immeasurable states, an observer is designed along with the controller to track a reference model which is a fixed point, a stable nonlinear system, or a chaotic system. For different premise variables between the plant and reference models, a robust approach is used to deal with the problem. The conditions for dealing with the stability of the overall error system are formulated into LMIs. Since the simultaneous solution to both the controller and observer gains with disturbances are not trivial, a two-step method is utilized. The methodology proposed above is applied to both continuous-time and discrete-time chaotic systems. Two well-known examples, the Chua’s circuit for continuous-time and Hénon map for discrete-time, are used in numerical simulations and DSP-based experiments. The results verify the validity of theoretical derivations.