# Isochronous Partitions for Region-Based Self-Triggered Control

## TL;DR

This paper introduces a novel region-based self-triggered control scheme for nonlinear systems, utilizing approximations of isochronous manifolds to determine sampling times based on state space partitions, with demonstrated efficiency through simulations.

## Contribution

It presents a new method for deriving regions and inter-event times using isochronous manifold approximations, addressing theoretical issues and providing an effective computational approach.

## Key findings

- Effective approximation of isochronous manifolds demonstrated
- Region-based STC scheme reduces sampling frequency
- Simulation results validate theoretical developments

## Abstract

In this work, we propose a region-based self-triggered control (STC) scheme for nonlinear systems. The state space is partitioned into a finite number of regions, each of which is associated to a uniform inter-event time. The controller, at each sampling time instant, checks to which region does the current state belong, and correspondingly decides the next sampling time instant. To derive the regions along with their corresponding inter-event times, we use approximations of isochronous manifolds, a notion firstly introduced in [1]. This work addresses some theoretical issues of [1] and proposes an effective computational approach that generates approximations of isochronous manifolds, thus enabling the region-based STC scheme. The efficiency of both our theoretical results and the proposed algorithm are demonstrated through simulation examples.