Robust Model Predictive Control for Piecewise Affine Systems

In this paper, we study a robust model predictive control (MPC) strategy for piecewise affine (PWA) systems with uncertainty that is described as a set of polytopic parameter-varying models in a polytope corresponding to each partition of the PWA systems. First, an infinite horizon MPC technique for guaranteeing robust stability is developed for uncertain PWA systems. According to the condition of the PWA system states, the sequence of piecewise linear feedback controller at each sampling time is derived on-line by solving a convex optimization problem involving linear matrix inequalities. The feasible PWA control law design can robustly stabilize the uncertain PWA systems. However, the on-line optimization problems may lead to a computational burden. Then we further propose an improved robust MPC algorithm. When the current state is outside of the region of PWA systems containing the origin, the proposed on-line robust MPC algorithm is utilized; once the current state enters the region with the origin, sequence attraction domains where the origin is included are constructed off-line one within another, and the explicit control laws corresponding to different attraction domains can drive the state to the origin. The two algorithms are illustrated with a numerical example. The simulation results show that both controller design methods can stabilize the PWA systems with polytopic uncertainty, and the improved algorithm can reduce the on-line computation cost.