Fairness of transitions in diagnosability analysis of hybrid systems

Requirement of reliable performance in complex mission critical systems have made online detection and isolation of failures a crucial task. Failure diagnosability has been widely studied for discrete event system (DES) models. It is however shown in this work, that the diagnosability condition which has been shown to be necessary and sufficient in the DES context fails to hold in a real-world example. This is because of the abstraction employed in formulating the DES models, which obliterates an important property of the transitions namely, their fairness. In this paper, failure diagnosability for fair discrete time hybrid system (DTHS) models is discussed. The modeling framework is defined and its properties for any given measurement limitation are discussed. A definition of diagnosability of these models is adopted from the literature on DES. Based on the measurement limited model, an algorithm for construction of a diagnoser is presented. Exploiting the fairness property, the diagnosability condition is suitably modified and its necessity and sufficiency properties are formally established. Further, an algorithm for transforming a hybrid system model to another comprising fair transitions only, has been developed using fixed point computation