Showing papers by "W. M. Wonham published in 1987"

Supervisory control of a class of discrete event processes

Abstract: This paper studies the control of a class of discrete event processes, i.e. processes that are discrete, asynchronous and possibly nondeter-ministic. The controlled process is described as the generator of a formal language, while the controller, or supervisor, is constructed from the grammar of a specified target language that incorporates the desired closed-loop system behavior. The existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language. Two examples are provided.

On the supermal controllable sublanguage of a given language

Abstract: The concept of controllable language has been shown to play a basic role in the existence theory of supervisory controls for discrete event processes. In this paper the supremal controllable sublanguage S of a given language L is characterized as the largest fixpoint of a monotone operator $\Omega $. In the case where the languages involved are regular it is shown that the fixpoint S can be computed as the limit of the (finite) sequence $\{ {K_j } \}$ given by $K_{j + 1} = \Omega (K_j )$, $K_0 = L$. An effective computational algorithm is developed, and three examples are provided for illustration.

Modular feedback logic for discrete event systems

Abstract: We examine a modular approach to the synthesis of state feedback controls for the problem of maintaining a predicate on the state set of a discrete dynamic system invariant. Dynamical systems are modeled by automata together with a mechanism for enabling and disabling a subset of state transitions. The basic problem of interest is to ensure by appropriate control action that a given predicate on the state set of the process remains invariantly true whenever it is initially satisfied. Assuming the predicate can be decomposed into the conjunction or disjunction of component predicates, we determine conditions under which it is possible to synthesize the appropriate control in a modular fashion.

State machines, temporal logic and control: A framework for discrete event systems

Abstract: A framework is proposed for investigating the verification and synthesis of controllers for real-time discrete event systems. In the framework, plants and controllers are modelled with extended state machines (ESMs), and a real-time temporal logic (RTL) is used for specification of required plant behaviour and for verifying that controllers satisfy their specifications. Controllers are implemented as tasks in a real-time distributed programming language. This paper discusses the issues of modelling and specification.

On Supervisory Control of Real-Time Discrete-Event Systems

Abstract: A discrete-event system G is modelled as the controlled generator of a formal language L(G), in the framework of Ramadge and Wonham. By means of the concepts of well-posed language and well-posed supervisor, it is suggested how this framework can accommodate certain real-time control constraints. Then it is shown that a closed-loop supervisory control has `correct' real-time behavior if and only if the supervisor is well-posed (with respect to time delay).