Compositional abstractions of networks of stochastic hybrid systems under randomly switched topologies

TL;DR

This paper develops compositional methods for creating abstractions of networks of stochastic hybrid systems with randomly switching topologies, enabling simplified controller design while ensuring system properties.

Contribution

It introduces conditions leveraging interconnection topology and dissipativity properties for constructing stochastic hybrid system abstractions in a compositional manner.

Findings

Successfully constructed stochastic hybrid system abstractions under random topology switching.

Demonstrated controller design on the abstraction and refinement to the original system.

Validated the approach with an example enforcing logic properties.

Abstract

In this work, we derive conditions under which abstractions of networks of stochastic hybrid systems can be constructed compositionally. Proposed conditions leverage the interconnection topology, switching randomly between P different interconnection topologies, and the joint dissipativity-type properties of subsystems and their abstractions. The random switching of the interconnection is modelled by a Markov chain. 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. Finally, we provide an example illustrating the effectiveness of the proposed results by designing a controller enforcing some logic properties over the interconnected abstraction and then refining it to the original interconnected system.