A Game-Theoretic approach to Fault Diagnosis of Hybrid Systems

TL;DR

This paper introduces a game-theoretic framework for fault diagnosis in hybrid systems, modeling the interaction between system faults and detection strategies using hybrid automata and analyzing the existence of effective diagnoser strategies.

Contribution

It proposes a novel game-theoretic approach to fault diagnosis in hybrid automata, including methods to determine and compute winning strategies for fault detection.

Findings

Existence of a diagnoser strategy can be decided for certain classes of hybrid automata.

A method to compute diagnoser strategies based on the game framework.

Application to o-minimal hybrid automata demonstrates practical feasibility.

Abstract

Physical systems can fail. For this reason the problem of identifying and reacting to faults has received a large attention in the control and computer science communities. In this paper we study the fault diagnosis problem for hybrid systems from a game-theoretical point of view. A hybrid system is a system mixing continuous and discrete behaviours that cannot be faithfully modeled neither by using a formalism with continuous dynamics only nor by a formalism including only discrete dynamics. We use the well known framework of hybrid automata for modeling hybrid systems, and we define a Fault Diagnosis Game on them, using two players: the environment and the diagnoser. The environment controls the evolution of the system and chooses whether and when a fault occurs. The diagnoser observes the external behaviour of the system and announces whether a fault has occurred or not. Existence of a winning strategy for the diagnoser implies that faults can be detected correctly, while computing such a winning strategy corresponds to implement a diagnoser for the system. We will show how to determine the existence of a winning strategy, and how to compute it, for some decidable classes of hybrid automata like o-minimal hybrid automata.