Research On Stability And Robustness Of Constrained Model Predictive Control

There exist extensively constraints in real control systems. Model predictive control (MPC) is a receding horizon control strategy, and provides a systematic approach to handle the constraints. However, in the presence of the constraints, both the control action of constrained MPC and the closed-loop system display nonlinearity, then how to guarantee the stability or robustness of the closed-loop system was a difficult problem once. The recent decade has seen a great progress in the theory of stability and robustness of constrained MPC. This paper is concerned with control design of constrained MPC for stability or robustness. The main results are given as follows:(1) The fundament of MPC is comprehensively summarized from its dominant idea, basic structure and essence. A survey for developing history and research status of MPC is provided.(2) The synthesis method of constrained MPC based on terminal constraint set and terminal cost function guaranteeing stability is studied, and it is shown that the method is in essence an infinite horizon MPC algorithm. A new design method is proposed using saturated state feedback controller as local stabilizing controller, and the corresponding terminal constraint set and terminal cost function can be computed by solving an LMI optimization problem separately. The control law can be obtained by solving an SOCP optimization problem. In contrast to existing algorithms, the proposed one provides a wider terminal constraint set, and then a wider stabilizable region. In addition, an algorithm is proposed to estimate the stabilizable region. Furthermore, An improved algorithm considering state soft constraints is presented.(3) The design method of dual mode MPC is discussed. An output feedback dual mode MPC algorithm based on ellipsoidal invariant set is proposed. Robust invariant set is introduced to obtain the terminal constraint set and feasible invariant set for the estimated state. Then this algorithm is extended to linear systems with bounded disturbance. Bounded stability of the closed-loop system is shown..(4) The synthesis problem of robust MPC for systems with model uncertainty is investigated. An infinite horizon min-max MPC algorithm for polytopic uncertain systems and structured feedback uncertain systems is respectively proposed. Robust stability of closed-loop system is shown. A state feedback control structure with saturation is used, and the control law can be obtained by solving an LMI optimization problem. In contrast to the algorithm using the linear state feedback control structure, the proposed one can make full use of the bound of...