Supervisory synthesis techniques for discrete event dynamical systems

Dynamical systems modeled at the level of abstraction in which a system is described in terms of states, and events, which occur at asynchronous instants of time and cause state transitions, are known as Discrete Event Dynamical Systems (DEDS's). In many man made systems--manufacturing systems, communication networks, computer systems, traffic systems etc.--various operational techniques, which depend on the state-event evolution of the system, are employed so that the behavior of the system is as desired. A formal theory using various transition based models for studying such systems, and techniques for synthesizing "supervisors" to guarantee the desired behavior of such systems, are presented in this thesis. The finite string behavior of a DEDS, also called a plant, is described by the language of a state machine (SM) used to model it. A supervisor is another SM which executes synchronously with the plant and thus controls its behavior. A supervisor can be constructed so that the controlled plant achieves the desired behavior if it is controllable and observable. Formulas for computing supremal controllable and supremal normal--a stronger notion of observability--are derived in a general setting. A computationally optimal algorithm for computing the supremal controllable language is obtained. The sequential or infinite string behavior of a plant is described by the infinite string language of the SM viewed as a Buchi automata. The problem of synthesizing supervisors for achieving the desired infinite behavior is reduced to that of controlling a finite behavior. Necessary and sufficient conditions under which a supervisor for restricting the sequential behavior of a partially observed plant to the desired one is obtained, and a method for constructing a minimally restrictive supervisor is presented. Notion of stability and stabilizability of the (finite and infinite string) behavior of a plant is defined, and necessary and sufficient conditions under which the behavior of a plant "stabilizes" to the desired one are obtained. Methods for constructing minimally restrictive stabilizing supervisors are provided. Behaviors described as certain properties of states (and not events) is also considered. A plant is described using predicates and predicate transformers. The notions of predicate based controllability and observability are introduced and the weakest controllable predicates are obtained as the extremal solutions of certain boolean equations.