Exploiting isochrony in self-triggered control

TL;DR

This paper introduces a novel method for computing execution instants in self-triggered control by exploiting isochronous manifolds, enabling resource-efficient control for any smooth system through homogenization.

Contribution

It presents a new technique using isochrony and homogenization to determine execution times in self-triggered control, applicable to all smooth control systems.

Findings

The isochrony-based method computes execution instants along all directions.

Homogenization extends the approach to any smooth control system.

Analysis shows improved resource efficiency over existing techniques.

Abstract

Event-triggered control and self-triggered control have been recently proposed as new implementation paradigms that reduce resource usage for control systems. In self-triggered control, the controller is augmented with the computation of the next time instant at which the feedback control law is to be recomputed. Since these execution instants are obtained as a function of the plant state, we effectively close the loop only when it is required to maintain the desired performance, thereby greatly reducing the resources required for control. In this paper we present a new technique for the computation of the execution instants by exploiting the concept of isochronous manifolds, also introduced in this paper. While our previous results showed how homogeneity can be used to compute the execution instants along some directions in the state space, the concept of isochrony allows us to compute the executions instants along every direction in the state space. Moreover, we also show in this paper how to homogenize smooth control systems thus making our results applicable to any smooth control system. The benefits of the proposed approach with respect to existing techniques are analyzed in two examples.