Reset Controller Synthesis by Reach-avoid Analysis for Delay Hybrid Systems

TL;DR

This paper introduces a method for synthesizing reset controllers in delay hybrid systems by leveraging reach-avoid set analysis, ensuring system objectives are met despite time delays.

Contribution

It extends reset controller synthesis to delay hybrid systems using reach-avoid analysis and convex optimization, addressing the impact of time delays.

Findings

Effective synthesis of reset controllers considering time delays.

Utilization of convex optimization for reach-avoid set computation.

Improved robustness of hybrid systems with delay considerations.

Abstract

A reset controller plays a crucial role in designing hybrid systems. It restricts the initial set and redefines the reset map associated with discrete transitions, in order to guarantee the system to achieve its objective. Reset controller synthesis, together with feedback controller synthesis and switching logic controller synthesis, provides a correct-by-construction approach to designing hybrid systems. However, time-delay is an inevitable factor in hybrid systems, which can degrade control performance and render verification certificates obtained by abstracting away time-delay invalid in practice. In this paper, we investigate this issue in a practical manner by taking time-delay into account. We propose an approach that reduces the synthesis of reset controllers to the generation of reach-avoid sets for the hybrid system under consideration, which can be efficiently solved using off-the-shell convex optimization solvers.