A Computational Approach to Bisimulation of Hybrid Dynamical Systems

TL;DR

This paper presents a novel algorithm for constructing minimal-state symbolic models bisimilar to hybrid dynamical systems, avoiding stability assumptions and time discretization, with applications demonstrated on an example.

Contribution

It introduces an algorithm that finds minimal bisimilar models for hybrid systems without requiring stability or time discretization.

Findings

Algorithm successfully computes minimal bisimilar models.

No stability assumptions or time discretization needed.

Effective application demonstrated on a practical example.

Abstract

The problem of finding a finite state symbolic model which is bisimilar to a hybrid dynamical system (HDS) and has the minimum number of states is considered. The considered class of HDS allows for discrete-valued inputs that only affect the jumps (events) of the HDS. Representation of the HDS in the form of a transition system is revisited in comparison with prior works. An algorithm is proposed for solving the problem which gives the bisimulation with the minimum number of states if it already exists and also a parameter of the algorithm is properly tuned. There is no need for stability assumptions and no time discretization is applied. The results are applied to an example