Self-triggered MPC for constrained linear systems and quadratic costs

Self-triggered control is a recently proposed control paradigm that abandons the conventional periodic sampling of outputs and updating of control values with the objective to reduce the utilization of communication resources, while still guaranteeing desirable closed-loop behaviour. Self-triggered control consists of two elements, namely a feedback controller that computes the next control input, and a triggering mechanism that determines what the next control update time will be. In this paper we present a self-triggered MPC strategy based on quadratic costs, which applies to discrete-time linear systems subject to state and input constraints. This self-triggered MPC law possesses three important features. First of all, the control law is designed such that a priori chosen (sub)optimality levels are guaranteed next to asymptotic stability and constraint satisfaction. Secondly, it is one of the first approaches, which addresses the joint design of both the feedback controller and the triggering mechanism. Thirdly, it realizes significant reductions in the usage of network resources and avoids bursts in communication. These beneficial features and various implementation aspects of the proposed self-triggered MPC strategy will be discussed in detail.