Membership-function-dependent model predictive control for nonlinear systems in a piecewise-fuzzy framework

Abstract

This paper is concerned with the membership-function-dependent model predictive control (MPC) problem for a class of Takagi-Sugeno (T-S) fuzzy systems with hard constraints. In order to design a set of membership-function-dependent controllers in the framework of MPC, the original T-S fuzzy systems are equivalently converted into a piecewise-fuzzy model by means of the partition method of the premise variable space. Then, instead of calculating vertices to construct the fuzzy MPC controller as adopted in the traditional T-S fuzzy control strategies, some staircase membership functions are employed to approximate the continuous membership functions, such that the information of membership functions can be adequately considered in the control synthesis to reduce the conservatism of the controller design. Furthermore, associated with the piecewise-fuzzy model, an online optimization problem based on the membership-function-dependent terminal constraint set is formulated in terms of the piecewise-Lyapunov-function-based MPC to calculate the feedback gains. Besides, by employing polynomial constraints based on the shape information of the membership functions, errors between the staircase membership functions and the original continuous membership functions are taken into account for facilitating the feasibility investigation and the stability analysis. Finally, two illustrative examples are used to illustrate the validity of the proposed membership-function-dependent MPC strategy.