The construction of controllable sublanguage of specification for DES via PCFs based inference

Abstract

The paper considers how methods of a logical inference search in the calculus of positively constructed formulas may be applied to represent and study discrete event systems. The formalisms of discrete event systems and positively constructed formulas are briefly described. A method for constructing a product of automata using constructive inference in the positively constructed formulas calculus is proposed. Based on the given specication on the behaviour of the system, a method for constructing a supremal controllable sublanguage of the specication is presented.

Analysis and Control of Partially Observed Discrete-Event Systems via Positively Constructed Formulas

“…The PCF-based procedure for checking controllability was suggested in [26]. It also allows one to construct supremal controllable sublanguage of uncontrollable specification such that it may be chosen as a new specification and be ensured by a proper supervisor.…”

“…This approach is applicable for nonmonotonic inferences and in similar situations where the previous history of the inference can change over time and become irrelevant. For example, the "from scratch" method is used for constructing the sublanguage K ↑C of an uncontrollable specification K [26]. In the PCF F Sub , for providing a sublanguage construction, a special operator * is employed.…”

“…Before designing a supervisor as a controller that ensures specification K msn , first, the supervisor existence criterion must be checked. By refuting the special PCF developed for controllability checking in [26], the prover Bootfrost established controllability of K msn . The observability of K msn is checked via inspection of automaton T H msn constructed using the PCF F Obs (2) (Section 3).…”

“…Our previous papers addressed how the basic problems of the supervisory control theory (SCT) [4] for logical DESs can be solved using the PCF-based technique. The issues considered so far include controllability checking to determine if a formal language restricting DES functioning may be guaranteed by a supervisor, a supremal controllable sublanguage of a given specification language construction, or a monolithic supervisor realization (e.g., [26]). This paper deals with partially observed DESs, in which the occurrence of some events is unavailable for observation.…”