Supervisory Control of Probabilistic Discrete Event Systems under Partial Observation
This work addresses control problems in systems with uncertainty and limited information, such as manufacturing or robotics, but is incremental as it extends existing discrete event system theory to probabilistic settings.
The paper tackles the supervisory control of probabilistic discrete event systems under partial observation by defining a probabilistic P-supervisor and proposing necessary and sufficient conditions (probabilistic controllability and observability) for its existence, with polynomial verification algorithms and an optimal control solution.
The supervisory control of probabilistic discrete event systems (PDESs) is investigated under the assumptions that the supervisory controller (supervisor) is probabilistic and has a partial observation. The probabilistic P-supervisor is defined, which specifies a probability distribution on the control patterns for each observation. The notions of the probabilistic controllability and observability are proposed and demonstrated to be a necessary and sufficient conditions for the existence of the probabilistic P-supervisors. Moreover, the polynomial verification algorithms for the probabilistic controllability and observability are put forward. In addition, the infimal probabilistic controllable and observable superlanguage is introduced and computed as the solution of the optimal control problem of PDESs. Several examples are presented to illustrate the results obtained.