Discrete Event System Methods for Control Problems Arising in Cyber-physical Systems.

Abstract

We consider two problems in cyber-physical systems. The first is that of dynamic fault diagnosis. Specifically, we assume that a plant model is available in the form of a discrete event system (DES) containing special fault events whose occurrences are to be diagnosed. Furthermore, it is assumed that there exist sensors that can be turned on or off and are capable of detecting some subset of the system’s non-faulty events. The problem to be solved consists of constructing a compact structure, called the most permissive observer (MPO), containing the set of all sequences of sensor activations that ensure the timely diagnosis of any fault event’s occurrence. We solve this problem by defining an appropriate notion of information state summarizing the information obtained from the past sequence of observations and sensor activations. The resulting MPO has a better space complexity than that of the previous approach in the literature. The second problem considered in this thesis is that of controlling vehicles through an intersection. Specifically, we wish to obtain a supervisor for the vehicles that is safe, non-deadlocking, and maximally permissive. Furthermore, we solve this problem in the presence of uncontrolled vehicles, bounded disturbances in the dynamics, and measurement uncertainty. Our approach consists of discretizing the system in time and space, obtaining a DES 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 yields maximally permissive memoryless supervisors for the original system and show that, under certain conditions, the resulting supervisor will be maximally permissive over the class of all supervisors, not merely memoryless ones. Our contributions are as follows. First, by constructing DES abstractions from continuous systems, we can leverage the supervisory control theory of DES, which is well-suited to finding maximally permissive supervisors under safety and non-blocking constraints. Second, we define different types of relations between transition systems and their abstractions and, for each relation, characterize the class of supervisors over which the supervisors obtained under our approach are maximally permissive.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/108720/1/edallal_1.pd