Passivity Degradation In Discrete Control Implementations: An Approximate Bisimulation Approach

TL;DR

This paper investigates how replacing a continuous controller with a discrete, symbolic implementation affects the passivity and stability of the closed-loop system, providing quantitative bounds and conditions for performance preservation.

Contribution

It introduces an approximate bisimulation framework to analyze passivity degradation in discrete control implementations of continuous systems.

Findings

Quantitative bounds on passivity degradation due to discretization

Conditions ensuring boundedness of the closed-loop system

Framework for compositional analysis of heterogeneous systems

Abstract

In this paper, we present some preliminary results for compositional analysis of heterogeneous systems containing both discrete state models and continuous systems using consistent notions of dissipativity and passivity. We study the following problem: given a physical plant model and a continuous feedback controller designed using traditional control techniques, how is the closed-loop passivity affected when the continuous controller is replaced by a discrete (i.e., symbolic) implementation within this framework? Specifically, we give quantitative results on performance degradation when the discrete control implementation is approximately bisimilar to the continuous controller, and based on them, we provide conditions that guarantee the boundedness property of the closed-loop system.