Compositional Symbolic Models for Networks of Incrementally Stable Control Systems

TL;DR

This paper presents a method for constructing symbolic models of interconnected nonlinear control systems that are incrementally stable, enabling correct-by-design control with guaranteed approximation accuracy.

Contribution

It introduces a compositional approach to build symbolic models for networks of incrementally stable control systems under small gain conditions.

Findings

Symbolic models can approximate networks of nonlinear control systems with arbitrary accuracy.

A compositional design method for quantization parameters is developed.

The approach relies on small gain theorem-type conditions for stability.

Abstract

Symbolic models have recently spurred the interest of the research community because they offer a correct-by-design approach to the control of embedded and cyber-physical systems. In this paper we address construction of symbolic models for networks of discrete-time nonlinear control systems. The main result of the paper shows that under some small gain theorem-type conditions, a network of symbolic models can be constructed which approximates a network of incrementally stable control systems in the sense of approximate bisimulation with any desired accuracy. Compositional design of quantization parameters of the symbolic models is also derived and based on the topological properties of the network.