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In cases where the discrete-event system model has an infinite or large state space, or when it is not completely specified a priori, applying the traditional off-line methods for computing the control policy may be impractical, if not infeasible. We adopt an online limited lookahead approach. Under this approach, the next control action is determined based on an N-step ahead projection of the system behavior and on one of two attitudes-conservative or optimistic. We extend this approach to incorporate knowledge of the system state in the computation. This has the potential of improving the efficiency of the computation as well as the quality of the control policy. There are five specific contributions presented in this paper: 1) a new algorithm for the online computation of supervisory controls with worst case complexity that is quadratic in the number of "expanded" states, 2) an algorithmic proof of the correctness of this …