Supervisory Control of Probabilistic Discrete Event Systems under Partial Observation

TL;DR

This paper develops a framework for supervisory control of probabilistic discrete event systems with partial observation, introducing probabilistic controllability and observability, and providing algorithms for their verification.

Contribution

It introduces the probabilistic P-supervisor concept and establishes necessary and sufficient conditions for control, along with polynomial algorithms for verification.

Findings

Probabilistic controllability and observability are characterized.

Polynomial algorithms for verification are proposed.

Optimal control solutions are derived for PDESs.

Abstract

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.