Robust approximate symbolic models for a class of continuous-time uncertain nonlinear systems via a control interface

TL;DR

This paper introduces a control interface approach to create robust approximate symbolic models for uncertain continuous-time nonlinear systems, avoiding complex discretization and ensuring stability and simulation relations.

Contribution

It proposes a novel control interface method and stability notion for linking continuous systems with discrete abstractions without time-space discretization.

Findings

The method ensures robust approximate simulation relations.

It guarantees practical stability of the augmented system.

Simulation examples demonstrate effectiveness.

Abstract

Discrete abstractions have become a standard approach to assist control synthesis under complex specifications. Most techniques for the construction of a discrete abstraction for a continuous-time system require time-space discretization of the concrete system, which constitutes property satisfaction for the continuous-time system non-trivial. In this work, we aim at relaxing this requirement by introducing a control interface. Firstly, we connect the continuous-time uncertain concrete system with its discrete deterministic state-space abstraction with a control interface. Then, a novel stability notion called $\eta$-approximate controlled globally practically stable, and a new simulation relation called robust approximate simulation relation are proposed. It is shown that the uncertain concrete system, under the condition that there exists an admissible control interface such that the augmented system (composed of the concrete system and its abstraction) can be made $\eta$-approximate controlled globally practically stable, robustly approximately simulates its discrete abstraction. The effectiveness of the proposed results is illustrated by two simulation examples.