Analysis And Synthesis Of T-S Fuzzy Control Systems Based On Piecewise Linear Systems Method

As nonlinear systems, it is not necessary to establish exact mathematical models for T-S fuzzy control systems and it is simple and convenient to design the controller and it has been widely studied and used among control engineering field. The piecewise linear systems can be used to analyze and design nonlinear systems with the existed results in linear systems. This thesis applies the theoretics of the piecewise linear systems to T-S fuzzy control systems. The groundwork is as follows:In the analysis of stability, this thesis makes use of continuous piecewise quadratic Lyapunov function instead of the global quadratic Lyapunov function to analyse the stability of T-S fuzzy control systems, solve the limitation of the methods before.Make the form of T-S fuzzy control systems into piecewise linear differential inclusions, make use of the optimal control method of piecewise linear systems to get the conclusion of T-S fuzzy systems. The optimal control of the piecewise linear systems can be characterized in terms of solution to the Hamilton-Jacobi-Bellman (H-J-B) equation. Based on H-J-B inequalities and piecewise quadratic Lyapunov function, the optimal control of the piecewise linear systems is converted to the problem of seeking upper and lower bounds of the cost function. The design of upper bound can be cast as a bilinear matrix inequalities (BMI) problem in which the feedback gain is a set of optimization parameters, and the lower bound computation can be solved as a semidefinite programming problem based on linear matrix inequalities (LMI). The BMI is a NP hard problem which can be solved effectively by genetic algorithm. A mixed algorithm that combines genetic algorithm and interior-point method is applied for solving the BMI problem. The results from numerical examples illustrate the effectiveness of the calculation method for the control law.