Stochastic self-triggered MPC for linear constrained systems under additive uncertainty and chance constraints

This paper presents a stochastic self-triggered model predictive control (MPC) scheme for linear systems with additive uncertainty, and with the states and inputs being subject to chance constraints. In the proposed control scheme, the succeeding sampling time instant and current control inputs are computed online by solving a formulated optimization problem. The chance constraints are reformulated into a deterministic fashion by leveraging the Cantelli's inequality. Under few mild assumptions, the online computational complexity of the proposed control scheme is similar to that of a nominal self-triggered MPC. Furthermore, initial constraints are incorporated into the MPC problem to guarantee the recursive feasibility of the scheme, and the stability conditions of the system have been developed. Finally, numerical examples are provided to illustrate the achievable performance of the proposed control strategy.