Identification and Control of Chaos Using Fuzzy Clustering and Sliding Mode Control in Unmodeled Affine Dynamical Systems

Abstract

In this paper, a combination of fuzzy clustering estimation and sliding mode control is used to control a chaotic system, which its mathematical model is unknown. It is assumed that the chaotic system has an affine form. At first, the nonlinear noninput part of the chaotic system is estimated by a fuzzy model, without using any input noise signal. Without loss of generality, it is assumed that chaotic behavior is appeared in the absence of input signal. In this case, the recurrent property of chaotic behavior is used for estimating its model. After constructing the fuzzy model, which estimates the noninput part of the chaotic system, control and on-line identification of the input-related section are applied. In this step, the system model will be estimated in normal form, such that the dynamic equations can be used in sliding mode control. Finally, the proposed technique is applied to a Lur’e-like dynamic system and the Lorenz system as two illustrative examples of chaotic systems. The simulation results verify the effectiveness of this approach in controlling an unknown chaotic system.