On optimal control of a class of partially observed discrete event systems

We are interested in a new class of optimal control problems for discrete event systems. We adopt the formalism of supervisory control theory (Proc. IEEE 77(1) (1989) 81) and model the system as a 4nite 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 4rst derive an observer for the partially unobservable FSM, which allows us to construct an approximation of the unobservable trajectory costs. We then de4ne the performance measure on this observer rather than on the original FSM itself. We then use the algorithm presented in Sengupta and Lafortune (SIAM J. Control Optim. 36(2) (1998)) to synthesize an optimal submachine of the C-observer. This submachine leads to the desired supervisor for the system. ? 2002 Elsevier Science Ltd. All rights reserved.