Symbolic Models for Nonlinear Control Systems: Alternating Approximate Bisimulations

TL;DR

This paper demonstrates that nonlinear control systems with disturbances can be approximated by symbolic models, facilitating control design, with simplified construction for linear cases, advancing the application of symbolic methods in control theory.

Contribution

It extends symbolic modeling to disturbed nonlinear control systems, providing a method to construct such models and simplifying the process for linear systems.

Findings

Symbolic models exist for incrementally globally asymptotically stable nonlinear systems with disturbances.

Constructing symbolic models for linear systems is straightforward.

The approach enhances control design tools for complex systems.

Abstract

Symbolic models are abstract descriptions of continuous systems in which symbols represent aggregates of continuous states. In the last few years there has been a growing interest in the use of symbolic models as a tool for mitigating complexity in control design. In fact, symbolic models enable the use of well known algorithms in the context of supervisory control and algorithmic game theory, for controller synthesis. Since the 1990's many researchers faced the problem of identifying classes of dynamical and control systems that admit symbolic models. In this paper we make a further progress along this research line by focusing on control systems affected by disturbances. Our main contribution is to show that incrementally globally asymptotically stable nonlinear control systems with disturbances admit symbolic models. When specializing these results to linear systems, we show that these symbolic models can be easily constructed.