Exponential Stability Based Design of Constrained Fuzzy Predictive Control

Abstract

Predictive control of nonlinear systems subject to output and input constraints is considered. A fuzzy model is used to predict the future behavior. Three new ideas are proposed here. First, an added constraint on the applied control action is used to ensure the decrease of a quadratic Lyapunov function, and so guarantee Lyapunov exponential stability of the closed-loop system. Second, the feasibility of the finite-horizon optimization problem with the added constraints is ensured based on off-line solution of a set of linear matrix inequalities (LMIs). Third, the proposed method is extended to observer-based feedback case. The novel stability method, which we call First Point Constraint Method, is compared to existing methods, such as the techniques based on the end-point constraints (Terminal Constraint Set), and the robust stability techniques based on the small gain theory. The proposed method ensures Lyapunov exponential stability, can be used for open loop unstable plants, and doesn’t need an auxiliary controller. Illustrative examples including the predictive control of a highly nonlinear continuous stirred tank reactor (CSTR) and the observer-based predictive control of a steam generator are discussed.