SOS-Based Control Methods Research And Application For T-S Fuzzy Systems

With the development of scientific theories and industrial technologies,the control systems encountered in industrial production and daily lives have become much more complex.And such various nonlinear systems have emerged to challenge to the control design methods.In recent decades,nonlinear control methods have also been developed,but most of the design procedures are complicated and specific.The T-S fuzzy model is an approximation of a nonlinear model through linear sub-models and membership functions.It can approximate nonlinear functions with various precisions.Therefore,the T-S fuzzy model can effectively represent nonlinear systems and provide solutions for nonlinear control.Therefore,it is of great significance to study the related control methods of T-S fuzzy systems.Based on sum of squares(SOS)approach,this thesis will mainly focus on the state feedback control of T-S fuzzy systems,and combine the specific engineering problems of the suspended floater following system.The main contributions are as follows:For the parking stabilization control problem of the suspended floater following system,a high-precision control strategy was designed using an SOS-based control Lyapunov function method.First,sufficient conditions in SOS terms for a positive definite function to become a CLF is presented.Then the control Lyapunov function is constructed by solving a series of SOS conditions.And the feedback controller in the form of non-parallel distributed compensation is designed.In addition,the semiglobal stabilization conditions on the operational domain are given in the same way as the research method of global stabilization.Both global and semiglobal stabilization control problems have been transformed into SOS convex optimization problems,and through the SOS convex optimization solution technology,polynomial stability conditions can be directly solved.Finally,the effectiveness of the proposed method is showed in simulation analysis.For the problem of high conservativeness of the membership function independent stability analysis method,a new polynomial-membership-function method is proposed to improve the robustness of the suspended floater following system.The membership functions transformation method is proposed by using the polynomial fitting method to approximate the original membership function of the T-S fuzzy systems,so that more membership functions information is involved in the stability analysis process to further reduce the conservatism.Then,the stability conditions are derived by using the obtained polynomial membership function and approximation errors.Finally,the effectiveness of this method is verified by simulation analysis of the abstract systems and the suspended floater following system with interference,and comparison with existing methods.