Internship Proposal (M2): Diagnosing Controller Synthesis

In discrete-event systems, diagnosis consists in determining in bounded time and with certainty whether a fault has occurred given a sequence of observations [4]. In fact, if some events internal to the system are not observable from outside, then a given observation sequence can correspond to several executions, some of which are faulty and other non-faulty. The simplest formalism for this problem is finite automata, and algorithms were given to check if a given model is diagnosable. However some systems carry an intrinsic ambiguity and the observations are not sufficient for diagnosing faults. Active diagnosis was suggested to overcome this issue [3, 2]. It consists in controlling the system by activating some events, and disabling some others, so that all induced executions can be diagnosed: whether a fault has occurred in the controlled system can be determined by looking at observations. The only objective in the active diagnosis problem is to control the system to make sure that any fault is diagnosed. But the computed controller does not guarantee any other property on the controlled system; for instance, a controller that makes sure that a fault always occurs is a possible solution to active diagnosis since it guarantees diagnosability. Some partial solutions were given, e.g. in [1], where it is required that the controller guarantees non-faulty behaviors with positive probability. In this internship, we suggest improving the active diagnosis problem to address this issue. We will consider diagnosability as an additional and secondary objective to be taken into account in controller synthesis with a give