Communication scheduling in robust self-triggered MPC for linear discrete-time systems

We consider a networked control system consisting of a physical plant, an actuator, a sensor, and a controller that is connected to the actuator and sensor via a communication network. The plant is described by a linear discrete-time system subject to additive disturbances. In order to reduce the required number of communications in the system, we propose a robust self-triggered model predictive controller based on rollout techniques that robustly asymptotically stabilizes a certain periodic sequence of sets in the state space while guaranteeing robust satisfaction of hard state and input constraints. At periodically occurring scheduling times, the self-triggered model predictive control algorithm determines the times at which the control input and plant measurement are updated in the time span until the next scheduling time. We establish a certain upper bound on the average sampling rate in the closed-loop system. Moreover, we show how increasing the asymptotic bound on the system state, which is a design parameter in the control scheme, can be used to further reduce the average number of communications in the system.