Compositional Construction of Finite State Abstractions for Stochastic Control Systems

TL;DR

This paper extends compositional finite-state abstraction techniques to stochastic control systems, enabling scalable controller synthesis for complex systems modeled by stochastic differential equations.

Contribution

It introduces a method to construct finite-state abstractions for stochastic systems using disturbance bisimulation, facilitating compositional analysis of interconnected systems.

Findings

Finite-state abstractions can be constructed for stochastic control systems.

Conditions for compositional abstraction of networked stochastic systems are provided.

The approach enables scalable controller synthesis for large stochastic systems.

Abstract

Controller synthesis techniques for continuous systems with respect to temporal logic specifications typically use a finite-state symbolic abstraction of the system. Constructing this abstraction for the entire system is computationally expensive, and does not exploit natural decompositions of many systems into interacting components. We have recently introduced a new relation, called (approximate) disturbance bisimulation for compositional symbolic abstraction to help scale controller synthesis for temporal logic to larger systems. In this paper, we extend the results to stochastic control systems modeled by stochastic differential equations. Given any stochastic control system satisfying a stochastic version of the incremental input-to-state stability property and a positive error bound, we show how to construct a finite-state transition system (if there exists one) which is disturbance bisimilar to the given stochastic control system. Given a network of stochastic control systems, we give conditions on the simultaneous existence of disturbance bisimilar abstractions to every component allowing for compositional abstraction of the network system.