Optimal Supervisory Control of Discrete

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.