# Compositional Abstraction of Large-Scale Stochastic Systems: A Relaxed Dissipativity Approach

## TL;DR

This paper introduces a less conservative compositional method for creating finite abstractions of large-scale stochastic systems, enabling analysis without requiring subsystem stabilizability.

## Contribution

It develops a relaxed, finite-step stochastic simulation framework that broadens the applicability of abstraction techniques to non-stabilizable subsystems.

## Key findings

- Successfully applied to three case studies
- Constructed finite MDPs for nonlinear stochastic systems
- Established less conservative compositionality conditions

## Abstract

In this paper, we propose a compositional approach for the construction of finite abstractions (a.k.a. finite Markov decision processes (MDPs)) for networks of discrete-time stochastic control subsystems that are not necessarily stabilizable. The proposed approach leverages the interconnection topology and a notion of finite-step stochastic storage functions, that describes joint dissipativity-type properties of subsystems and their abstractions, and establishes a finite-step stochastic simulation function as a relation between the network and its abstraction. To this end, we first develop a new type of compositionality conditions which is less conservative than the existing ones. In particular, using a relaxation via a finite-step stochastic simulation function, it is possible to construct finite abstractions such that stabilizability of each subsystem is not necessarily required. We then propose an approach to construct finite MDPs together with their corresponding finite-step storage functions for general discrete-time stochastic control systems satisfying an incremental passivablity property. We also construct finite MDPs for a particular class of nonlinear stochastic control systems. To demonstrate the effectiveness of the proposed results, we apply our results on three different case studies.