Self-Triggered Control for Near-Maximal Average Inter-Sample Time

TL;DR

This paper introduces a novel self-triggered control method that maximizes average inter-sample time while maintaining control performance, using finite-state abstractions and mean-payoff game solutions.

Contribution

It presents a new approach to design self-triggered policies that optimize sampling intervals with proven bounds, improving over existing methods.

Findings

Achieves near-maximal average inter-sample time under performance constraints.

Uses finite-state abstraction and mean-payoff games for policy synthesis.

Provides bounds and refinement techniques for optimality.

Abstract

Self-triggered control (STC) is a sample-and-hold control method aimed at reducing communications within networked-control systems; however, existing STC mechanisms often maximize how late the next sample is, and as such they do not provide any sampling optimality in the long-term. In this work, we devise a method to construct self-triggered policies that provide near-maximal average inter-sample time (AIST) while respecting given control performance constraints. To achieve this, we rely on finite-state abstractions of a reference event-triggered control, in which early triggers are also allowed. These early triggers constitute controllable actions of the abstraction, for which an AIST-maximizing strategy can be computed by solving a mean-payoff game. We provide optimality bounds, and how to further improve them through abstraction refinement techniques.