A game-theoretic approach to fault diagnosis and identification of hybrid systems

Physical systems can fail. For this reason the problem of identifying and reacting to faults has received a lot of 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 modelled neither by using a formalism with continuous dynamics only nor by a formalism including only discrete dynamics. We model hybrid systems as Hybrid Automata and add distinguished actions to describe faults. We define a Fault Identification Game on them, using two players: the environment and the identifier. The environment controls the evolution of the system and chooses whether and when a fault occurs. The identifier observes the external behaviour of the system and announces whether a fault has occurred or not. Existence of a winning strategy for the identifier implies that faults can be detected correctly, while computing such a winning strategy corresponds to implementing an identifier for the system. We will show how to determine the existence of a winning strategy, and how to compute it, for all decidable classes of hybrid automata that admit a finite bisimulation quotient.