Self-triggered control for constrained systems: a contractive set-based approach (Technical report)

TL;DR

This paper introduces a self-triggered control method for constrained discrete-time systems using set-invariance theory, constructing a graph of polyhedral sets to optimize control updates and reduce computational effort.

Contribution

It presents a novel approach combining set-invariance with graph search algorithms to determine optimal inter-event times in self-triggered control schemes.

Findings

Effective control update scheduling demonstrated through numerical example

Reduction in control update frequency without compromising system constraints

Framework applicable to various constrained control systems

Abstract

In this paper, a self-triggered control scheme for constrained discrete-time control systems is presented. The key idea of our approach is to construct a transition system or a graph structure from a collection of polyhedral sets, which are generated based on the notion of {set-invariance theory}. The inter-event time steps are then determined through a standard graph search algorithm to obtain the minimal total cost to a terminal state. The proposed strategy is illustrated through a numerical example.