On stability of model predictive control with finite-control-set constraints and disturbances

This paper investigates the stability issues of model predictive control (MPC) for discrete-time linear systems with state and finite control set (FCS) constraints subject to time-varying disturbances. A new FCS-MPC design and analysis framework is developed using the disturbance estimation approaches and the tool of robust positive invariant (RPI) set sequence. It encompasses a discrete-time exogenous signal observer that helps characterize the estimated dynamics within well-defined bounds and a quantized control law that adheres to both state and input constraints. The practical asymptotical stability of the resulting closed-loop system is shown to be guaranteed, and the tracking error remains uniformly bounded. Finally, simulation results of a numerical example validate the effectiveness of the proposed method.