Robust self-triggered MPC for constrained linear systems

In this paper we propose a robust self-triggered model predictive control algorithm for linear systems with additive bounded disturbances and hard constraints on the inputs and state. In self-triggered control, at every sampling instant the time until the next sampling instant is computed online based on the current state of the system. The goal is to achieve a low average sampling rate, thereby minimizing communication in the control system and possibly reducing the number of control updates as is required in sparse control applications. Naturally, and intentionally, our approach leads to long spans of time in which the plant is controlled in an open-loop fashion. Especially for unstable plants or large disturbances this necessitates taking into account the disturbance characteristics in the design of the control law in order to prevent constraint violation in the closed-loop system. We use constraint tightening methods as proposed in Tube Model Predictive Control to guarantee robust constraint satisfaction. The self-triggered controller is shown to stabilize a robust invariant set in the state space for the closed-loop system.