A deterministic optimal control theory for discrete event systems

In certain discrete event applications it may be desirable to find a particular controller, within the set of acceptable controllers, which extremises some quantitative performance measure. In this paper we propose a theory of optimal control to meet such design requirements for deterministic systems. The discrete event system (DES) is modelled by a regular language. Event and cost functions are defined which induce costs on controlled system behaviour. The event costs associated with the system behaviour can only be reduced, in general, by increasing the control costs. Thus it is nontrivial to find the optimal amount of control to use and consequently the formulation captures the fundamental tradeoff motivating classical optimal control. Results on the existence and computability of minimally restrictive optimal controllers are presented. Such controllers are also polynomially computable under certain assumptions. It is shown that this framework subsumes the prior graph-theoretic formulation