Model predictive control for T‐S fuzzy Markovian jump systems using dynamic prediction optimization

Abstract

Abstract This paper addresses model predictive control (MPC) for constrained discrete‐time Takagi–Sugeno fuzzy Markovian jump systems (FMJSs) with imperfectly matched premise rules. To balance computational efficiency, control performance, and feasible regions, a dynamic prediction optimizing (DPO)‐MPC framework is proposed, incorporating mode‐dependent state feedback fuzzy controllers and perturbation variables generated by predictive dynamics. The design involves two stages: (1) solving a min‐max problem to derive terminal constraint sets and feedback gains and (2) optimizing perturbations online to expand the feasible region of system state. Matrix factorization enables off‐line computation of dynamic feedback gains, while online optimization adjusts the controller state to steer the system from initial to terminal regions. Recursive feasibility and mean square stability are rigorously proven, and a robot arm example validates the method's efficacy.