This paper studies the supervisory control of partially observed quantitative discrete event systems (DESs) under the fixed-initial-credit energy objective. A quantitative DES is modeled by a weighted automaton whose event set is partitioned into a controllable event set and an uncontrollable event set. Partial observation is modeled by a mapping from each event and state of the DES to the corresponding masked event and masked state that are observed by a supervisor. The supervisor controls the DES by disabling or enabling any controllable event for the current state of the DES, based on the observed sequences of masked states and masked events. We model the control process as a two-player game played between the supervisor and the DES. The DES aims to execute the events so that its energy level drops below zero, while the supervisor aims to maintain the energy level above zero. We show that the proposed problem is reducible to finding a winning strategy in a turn-based reachability game.

In this paper, we formulate an optimal stabilization problem of quantitative discrete event systems (DESs) under partial observation. A DES under partial observation is a system where its behaviors cannot be completely observed by a supervisor. In our framework, the supervisor observes not only masked events but also masked states. Our problem is then to synthesize a supervisor that drives the DES to a given target state with the minimum cost based on the detected sequences of masked events and states. We propose an algorithm for deciding the existence of an optimal stabilizing supervisor, and compute it if it exists.

This paper considers an optimal stabilization problem of quantitative discrete event systems (DESs) under the influence of disturbances. We model a DES by a deterministic weighted automaton. The control cost is concerned with the sum of the weights along the generated trajectories reaching the target state. The region of weak attraction is the set of states of the system such that all trajectories starting from them can be controlled to reach a specified set of target states and stay there indefinitely. An optimal stabilizing controller is a controller that drives the states in this region to the set of target states with minimum control cost and keeps them there. We consider two control objectives: to minimize the worst-case control cost (1) subject to all enabled trajectories and (2) subject to the enabled trajectories starting by controllable events. Moreover, we consider the disturbances which are uncontrollable events that rarely occur in the real system but may degrade the control performance when they occur. We propose a linearithmic time algorithm for the synthesis of an optimal stabilizing controller which is robust to disturbances.