Stable Model Predictive Control of Fuzzy Affine Systems with Input and State Constraints

Abstract

In this paper, a fuzzy affine model, which is more capable of representing strongly nonlinear dynamics, is used for predictive controller design. Based on piecewise quadratic Lyapunov functions, the proposed fuzzy affine model predictive control approach can ensure both the closed-loop system stability and the satisfactory transient control performance even under input and state constraints. With the help of partitioned degenerate ellipsoids and S-procedure, the large terminal invariant set of a fuzzy affine system can be achieved offline by solving a convex semi-definite programming problem subject to some linear matrix inequalities, rather than the non-convex bilinear matrix inequalities as in conventional fuzzy affine model based control. Then with the associated terminal cost, the resulting online open-loop predictive control approach can be formulated as a standard quadratic programming problem, which is readily solvable. Simulation results have demonstrated the performance of the proposed approach.