Sensor fault detection and isolation: a game theoretic approach

This paper studies sensor fault detection using a game theoretic approach. Sensor fault detection is considered as change point analysis in the coefficients of a regression model. A new method for detecting faults, referred to as two-way fault detection, is introduced which defines a game between two players, i.e. the fault detectors. In this new strategic environment, assuming that the independent states of the regression model are known, the test statistics are derived and their finite sample distributions under the null hypothesis of no change are derived. These test statistics are useful for testing the fault existence, as well as, the pure and mixed Nash equilibriums are derived for at-most-one-change and epidemic change models. A differential game is also proposed and solved using the Pontryagin maximum principle. This solution is useful for studying the fault detection problem in unknown state cases. Kalman filter and linear matrix inequality methods are used in finding the Nash equilibrium for the case of unknown states. Illustrative examples are presented to show the existence of the Nash equilibriums. Also, the proposed fault detection scheme is numerically evaluated via its application on a practical system and its performance is compared with the cumulative sum method

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

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