Discrete Event System Methods for Control Problems Arising in Cyber-physical Systems
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We consider two problems in cyber-physical systems. The first is that of dynamic fault diagnosis, where a plant model is available in the form of a discrete event system containing special fault events whose occurrence we would like to diagnose. There exist sensors that can be turned on/off and can detect some subset of the system's non-faulty events. We present an approach to construct a compact structure containing the set of all sequences of sensor activations that ensure that any fault event's occurrence will be correctly diagnosed within some finite number of event occurrences. The second problem is that of controlling a set of vehicles through an intersection, in the presence of bounded disturbances in the dynamics, measurement uncertainty, and uncontrolled vehicles. The objective is to design a supervisor for the controlled vehicles that is collision-free, ensures that all vehicles eventually cross the intersection, and interferes with the drivers only when necessary to avoid collisions. We solve this problem by discretizing the system in time and space, obtaining a discrete event system abstraction, solving for maximally permissive supervisors in the abstracted domain, and refining the supervisor to one for the original, continuous, problem domain. We provide general results under which this approach will result in the obtention of maximally permissive supervisors for the original system.