We are interested in a new 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 then define the performance measure on this observer rather than on the original FSM itself. We then use the algorithm presented in Sengupta & Lafortune (Siam J. Control Optimi. 36(2) (1998) to synthesize an optimal submachine of the C-observer. This submachine leads to the desired supervisor for the system.