\(H_{\infty}\) variable universe adaptive fuzzy control for chaotic system
The \(H_{\infty}\) control technique is combined with an adaptive control algorithm and the fuzzy approximate method in this study to achieve a desired attenuation of disturbance due to an approximation error and an external disturbance in a class of nonlinear system under a large uncertainty or unknown variation in plant parameter and structure. More precisely, the system under consideration is of the form: \[ \dot x= Ax+B(f(x)+g(x)u+d), \] \[ y=C^Tx \] where \((A,B,C)\) is the canonical minimal realization of a transfer function and \(f(x)\) and \(g(x)\) are unknown but bounded functions, \(u\in{\mathbb R}, y\in{\mathbb R}\) are control input and output of the system, respectively. \(d\) denotes an external bounded disturbance which is unknown. A new adaptive fuzzy control algorithm is proposed in the study, so that not only the stability of the adaptive fuzzy control system is guaranteed but also the influence of matching error and external disturbance on the tracking error is attenuated to an arbitrarly desired level via an \(H_{\infty}\) tracking design technique. The proposed design method attempts to combine the attenuation technique, a fuzzy logical approximation method and an adaptive algorithm for the robust tracking control design. The simulation results of the Duffing chaotic system are given to confirm that the control algorithm is feasible for practical application.
scientific article; zbMATH DE number 2167920