A generic approach to the control of discrete event systems

Abstract

In this paper, we present extensions of the framework of the µ-calculus which allow us to handle in a very generic and extensible way many control problems. The fundamental new tool is a division operator, and two new modalities are given as examples which allow us to handle observability and distinguishability. Furthermore, all this gives rise to a method for the synthesis of controllers which is implemented in a tool presented here.

Quotient-based control synthesis for partially observed non-deterministic plants with mu-calculus specifications

“…The problem of control of a deterministic plant subject to a µ-calculus specification was first addressed by Arnold, Vincent, and Walukiewicz in [3], which led to subsequent extensions in [2], [6].…”

“…This lets us handle the plant nondeterminism and state-based controllability and observability requirements in a simple manner. On the other hand, in [3], [2], [6] µ-calculus quotienting is performed at the level of their alternating tree automata representations and controllability and observability requirements are imposed separately on the quotiented formula. As a result, these techniques are only applicable for deterministic plants and can only consider controllability and observability requirements that are independent of plant states.…”

“…extension includes a new "observational" formula expression. Analogously, [3] introduced "loop-µ-calculus" extension to capture unobservable events; further extensions µ-calculus (CONV-modality) and alternating tree automata were later proposed in [2] and [6] for capturing indistinguishable events. [12], [11] also presented an automata-theoretic quotienting approach for supervisor synthesis for enforcing µ-calculus specifications.…”

“…We avoid capturing the supervisor existence as part of the specification logic and delegate that to the satisfiability of the quotiented property. Furthermore, as with [3], [2], [6], the work in [11] is limited to deterministic plants.…”