H∞ tracking control for coupled spatio-temporal chaos with uncertain model based on fuzzy observers

Abstract

Due to the interactions among coupled spatio_temporal subsystems and th e model uncertainties, it is difficult to achieve tracking control for coupled s patio_temporal chaos with uncertain model. However, every subsystem of the coupl e d spatio_temporal chaos is approximated by a set of fuzzy models. Considering th at the st ates of the subsystems are not all available, a set of fuzzy observers are propo sed to estimate these states. Because it is very difficult to exactly eliminate many parameters and dynamic characters of the chaotic system, that is to say, the s yst em model is uncertain, there can be deviation between the fuzzy models and the real chaotic system due to approximation error. Based on these fuzzy models and observers, considering the model uncertainties, a H∞ fuzzy tracking contro l scheme is proposed, and the robust tracking control for the coupled spatio_tem pora l chaos with the uncertain model is achieved by the above scheme. A linear matri x inequali ty is employed to represent the feedback controller, the parameters of the contr oller being obtained by using the convex optimization techniques of linear matri x inequalites. The stability of the system is guaranteed and the tracking performances are tested by a simul ation example.