A Game-Theoretic approach to Fault Diagnosis of Hybrid Systems

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.