Stochastic self-triggered model predictive control for linear systems with probabilistic constraints

A stochastic self-triggered model predictive control (SSMPC) algorithm is proposed for linear systems subject to exogenous disturbances and probabilistic constraints. The main idea behind the self-triggered framework is that at each sampling instant, an optimization problem is solved to determine both the next sampling instant and the control inputs to be applied between the two sampling instants. Although the self-triggered implementation achieves communication reduction, the control commands are necessarily applied in open-loop between sampling instants. To guarantee probabilistic constraint satisfaction, necessary and sufficient conditions are derived on the nominal systems by using the information on the distribution of the disturbances explicitly. Moreover, based on a tailored terminal set, a multi-step open-loop MPC optimization problem with infinite prediction horizon is transformed into a tractable quadratic programming problem with guaranteed recursive feasibility. The closed-loop system is shown to be stable. Numerical examples illustrate the efficacy of the proposed scheme in terms of performance, constraint satisfaction, and reduction of both control updates and communications with a conventional time-triggered scheme.