Switching Controller Synthesis for Delay Hybrid Systems under Perturbations

TL;DR

This paper introduces a new model called delay hybrid automata to handle delays in hybrid systems and proposes a robust switching controller synthesis method to ensure safety despite perturbations.

Contribution

It develops a novel delay hybrid automata model and a controller synthesis approach based on differential invariants and backward reachable sets for delay systems.

Findings

Successfully modeled delays in hybrid systems with delay hybrid automata

Proposed a controller synthesis method ensuring safety under perturbations

Validated approach through implementation and case studies

Abstract

Delays are ubiquitous in modern hybrid systems, which exhibit both continuous and discrete dynamical behaviors. Induced by signal transmission, conversion, the nature of plants, and so on, delays may appear either in the continuous evolution of a hybrid system such that the evolution depends not only on the present state but also on its execution history, or in the discrete switching between its different control modes. In this paper we come up with a new model of hybrid systems, called \emph{delay hybrid automata}, to capture the dynamics of systems with the aforementioned two kinds of delays. Furthermore, based upon this model we study the robust switching controller synthesis problem such that the controlled delay system is able to satisfy the specified safety properties regardless of perturbations. To the end, a novel method is proposed to synthesize switching controllers based on the computation of differential invariants for continuous evolution and backward reachable sets of discrete jumps with delays. Finally, we implement a prototypical tool of our approach and demonstrate it on some case studies.