Modeling, analysis and control of centralized and decentralized logical discrete -event systems.
G. Barrett, Stéphane Lafortune · Deep Blue (University of Michigan) · 1999
Centralized and decentralized control of logical discrete-event systems are considered. A fundamental relationship between the controllability of a language in the Supervisory Control Theory initiated by Ramadge and Wonham and bisimulation of automata models is derived. The theoretical results relating bisimulation to controllability support an efficient solution to the Basic Supervisory Control Problem; it is possible to find a partition which represents the supremal controllable sublanguage of an automaton with respect to the language of another automaton and a set of events in a worst-case running time of O(m log(n)), where m is the number of transitions and n is the number of states. Utilizing the bisimulation property of language controllability and derived relationships between automata languages and input/output finite-state machine behaviors, a precise relationship is formally derived between Supervisory Control Theory and the system-theoretic problem called Strong Input/Output FSM Model Matching. Specifically, it is proven that in deterministic settings instances of each problem can be mapped to the other framework and solved. The decentralized control problem for discrete-event systems addressed is that of several communicating supervisory controllers, each with different information, working in concert to exactly achieve a given legal sublanguage of the uncontrolled system's language model. A novel framework is presented for dealing with this class of problems, and existence results are given for the cases of when controllers do and do not anticipate future communications. Existence of one-way communication policies is derived. Several conditions for optimality of communication policies are presented, and it is shown that a useful concept of state generally does not exist to assist synthesis in decentralized control problems with communication. A synthesis procedure is given for the constrained case when controllers do not anticipate communications (myopic), and the resulting communication policies, when they exist, are optimal in a particular sense.