Fast Self-Triggered MPC for Constrained Linear Systems with Additive Disturbances

This article proposes a robust self-triggered model predictive control (MPC) algorithm for a class of constrained linear systems subject to bounded additive disturbances, in which the intersampling time is determined by a fast convergence self-triggered mechanism. The main idea of the self-triggered mechanism is to select a sampling interval so that a rapid decrease in the predicted costs associated with optimal predicted control inputs is guaranteed. This allows for a reduction in the required computation without compromising performance. By using a constraint tightening technique and exploring the nature of the open-loop control between sampling instants, a set of minimally conservative constraints is imposed on nominal states to ensure robust constraint satisfaction. A multistep open-loop MPC optimization problem is formulated, which ensures recursive feasibility for all possible realizations of the disturbance. The closed-loop system is guaranteed to satisfy a mean-square stability condition. To further reduce the computational load, when states reach a predetermined neighborhood of the origin, the control law of the robust self-triggered MPC algorithm switches to a self-triggered local controller. A compact set in the state space is shown to be robustly asymptotically stabilized. Numerical comparisons are provided to demonstrate the effectiveness of the proposed strategies.