Indirect Model Reference Fuzzy Control of SISO Fractional Order Nonlinear Chaotic Systems

This paper presents a novel indirect model reference fuzzy control for the control of a fractional order chaotic nonlinear dynamic system. The proposed control scheme benefits from a fractional order reference model which has more degrees of freedom. Takagi-Sugeno fuzzy model is used to model the nonlinear dynamic system under control. Some adaption laws are proposed to estimate the parameters of the Takagi-Sugeno fuzzy model. The stability of the proposed structure and the proposed adaptation laws are proved using a novel Lyapunov function. In order to show the implementability and effectiveness of the proposed controller, it is simulated on the control of a fractional order chaotic Duffing oscillator.