Optimal Supervisory Control of Discrete Event Dynamical Systems 1 , 2

We formalize the notion of optimal supervisory control of discrete event dynamical systems (DEDS's) in the framework of Ramadge and Wonham. A DEDS is modeled as a state machine, and is controlled by disabling some of its transitions. We de ne two types of cost functions: a cost of control function corresponding to disabling transitions in the state machine, and a penalty of control function corresponding to reaching some undesired states, or not reaching some desired states in the controlled system. The control objective is to design an optimal control mechanism, if it exists, so that the net cost is minimized. Since a DEDS is represented as a state machine|a directed graph|network ow techniques are naturally applied for designing optimal supervisors. We also show that our techniques can be used for solving supervisory control problems under complete as well as partial observation. In particular, we obtain, for the rst time, techniques for computing the supremal controllable and normal sublanguage, and the in mal controllable and normal/observable superlanguage without having to perform alternate computations of controllable and normal/observable languages.

[1]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[2]  P. Ramadge,et al.  On the supremal controllable sublanguage of a given language , 1984, The 23rd IEEE Conference on Decision and Control.

[3]  P. Ramadge,et al.  Modular feedback logic for discrete event systems , 1987 .

[4]  P. Ramadge,et al.  Supervisory control of a class of discrete event processes , 1987 .

[5]  John N. Tsitsiklis,et al.  On the control of discrete-event dynamical systems , 1987, 26th IEEE Conference on Decision and Control.

[6]  C. Desclaux,et al.  Supervisory control of discrete-event processes with partial observations , 1988 .

[7]  Walter Murray Wonham,et al.  On observability of discrete-event systems , 1988, Inf. Sci..

[8]  K. Passino,et al.  On the optimal control of discrete event systems , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[9]  M. Heymann,et al.  On stabilization of discrete-event processes , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[10]  R. D. Brandt,et al.  Formulas for calculating supremal controllable and normal sublanguages , 1990 .

[11]  A. Willsky,et al.  Observability of discrete event dynamic systems , 1990 .

[12]  Panos J. Antsaklis,et al.  Stability and stabilizability of discrete event dynamic systems , 1991, JACM.

[13]  S. Marcus,et al.  On controllability and normality of discrete event dynamical systems , 1991 .

[14]  W. Wonham,et al.  The infimal prefix-closed and observable superlanguage of given language , 1991 .

[15]  Jana Kosecka,et al.  Control of Discrete Event Systems , 1992 .

[16]  Vijay K. Garg,et al.  A State-Variable Approach for Controlling Discrete Event Systems with Infinite States , 1992, 1992 American Control Conference.

[17]  Ratnesh Kumar.  Supervisory synthesis techniques for discrete event dynamical systems , 1992 .

[18]  Stéphane Lafortune,et al.  A graph-theoretic optimal control problem for terminating discrete event processes , 1992, Discret. Event Dyn. Syst..

[19]  Michael Heymann,et al.  On optimal attraction in discrete-event processes , 1993, Inf. Sci..

[20]  S. Marcus,et al.  Language stability and stabilizability of discrete event dynamical systems , 1993 .

[21]  Vijay K. Garg,et al.  Predicates and predicate transformers for supervisory control of discrete event dynamical systems , 1993, IEEE Trans. Autom. Control..