Symbolic Control: Unveiling Free Robustness Margins

TL;DR

This paper develops methods to compute and utilize robustness margins in symbolic control systems, enhancing their ability to handle system perturbations while maintaining desired behaviors.

Contribution

It introduces constructive procedures for calculating both uniform and non-uniform robustness margins in symbolic models, linking margin tightness to reachability techniques.

Findings

Symbolic models inherently possess free robustness margins.

Constructive methods for computing state and input dependent margins.

Robustness margin tightness depends on reachability analysis accuracy.

Abstract

This paper addresses the challenge of ensuring robustness in the presence of system perturbations for symbolic control techniques. Given a discrete-time control system that is related to its symbolic model by an alternating simulation relation. In this paper, we focus on computing the maximum robustness margin under which the symbolic model remains valid for a perturbed-version of the discrete-time control system. We first show that symbolic models are inherently equipped with a certain free robustness margins. We then provide constructive procedures to compute uniform and non-uniform (state and input dependent) robustness margins. We also show that the tightness of the robustness margin depends on the tightness of the reachability technique used to compute the symbolic model. We then explain how the computed robustness margin can be used for the sake of controller synthesis. Finally, we present two illustrative examples to demonstrate the effectiveness of our approach.