# Compositional abstraction and safety synthesis using overlapping symbolic models

## TL;DR

This paper introduces a compositional method for abstraction and safety synthesis of nonlinear systems using overlapping symbolic models, reducing complexity and conservatism compared to existing approaches.

## Contribution

It develops a novel compositional safety synthesis technique leveraging overlapping symbolic subsystems for nonlinear systems.

## Key findings

- Significant reduction in computational complexity.
- Reduced conservatism compared to non-overlapping approaches.
- Effective safety guarantees for complex nonlinear systems.

## Abstract

In this paper, we develop a compositional approach to abstraction and safety synthesis for a general class of discrete time nonlinear systems. Our approach makes it possible to define a symbolic abstraction by composing a set of symbolic subsystems that are overlapping in the sense that they can share some common state variables. We develop compositional safety synthesis techniques using such overlapping symbolic subsystems. Comparisons, in terms of conservativeness and of computational complexity, between abstractions and controllers obtained from different system decompositions are provided. Numerical experiments show that the proposed approach for symbolic control synthesis enables a significant complexity reduction with respect to the centralized approach, while reducing the conservatism with respect to compositional approaches using non-overlapping subsystems.