From Dissipativity Theory to Compositional Abstractions of Interconnected Stochastic Hybrid Systems

TL;DR

This paper develops a framework for creating simplified stochastic hybrid system models from complex interconnected systems using dissipativity theory, enabling easier controller design without requiring identical noise processes.

Contribution

It introduces new conditions for compositional abstraction of stochastic hybrid systems considering nonlinearities and differing noise processes, advancing the state of the art in system simplification.

Findings

Effective abstraction construction for stochastic hybrid systems.

Applicability to systems with nonlinearities satisfying quadratic inequalities.

Numerical examples demonstrating the approach's effectiveness.

Abstract

In this work, we derive conditions under which compositional abstractions of networks of stochastic hybrid systems can be constructed using the interconnection topology and joint dissipativity-type properties of subsystems and their abstractions. In the proposed framework, the abstraction, itself a stochastic hybrid system (possibly with a lower dimension), can be used as a substitute of the original system in the controller design process. Moreover, we derive conditions for the construction of abstractions for a class of stochastic hybrid systems involving nonlinearities satisfying an incremental quadratic inequality. In this work, unlike existing results, the stochastic noises and jumps in the concrete subsystem and its abstraction need not to be the same. We provide examples with numerical simulations to illustrate the effectiveness of the proposed dissipativity-type compositional reasoning for interconnected stochastic hybrid systems.