We are interested in a class of optimal control problems for discrete event systems (DES). We adopt the formalism of supervisory control theory and model the system as a finite state machine (FSM). Our control problem is characterized by the presence of uncontrollable as well as unobservable events, the notion of occurrence and control costs for events and a worst-case objective function. We first derive an observer for the partially unobservable FSM, which allows us to construct an approximation of the unobservable trajectory costs. We define the performance measure on this observer rather than on the original FSM itself. Further, we use the algorithm of Sengupta and Lafortune (1998) to synthesize an optimal submachine of the observer. This submachine leads to the desired supervisor for the system