Metrization and Simulation of Controlled Hybrid Systems

TL;DR

This paper introduces a unified metric framework for controlled hybrid systems enabling accurate simulation and analysis of their behaviors, including complex phenomena like Zeno events.

Contribution

It develops a novel state space metric and a convergent numerical simulation algorithm for controlled hybrid systems, addressing limitations of previous methods.

Findings

The simulation algorithm converges uniformly with a known rate.

The metric effectively captures hybrid system behaviors including Zeno phenomena.

Benchmark examples demonstrate the practical utility of the approach.

Abstract

The study of controlled hybrid systems requires practical tools for approximation and comparison of system behaviors. Existing approaches to these problems impose undue restrictions on the system's continuous and discrete dynamics. Metrization and simulation of controlled hybrid systems is considered here in a unified framework by constructing a state space metric. The metric is applied to develop a numerical simulation algorithm that converges uniformly, with a known rate of convergence, to orbitally stable executions of controlled hybrid systems, up to and including Zeno events. Benchmark hybrid phenomena illustrate the utility of the proposed tools.