An Approach for Supervisor Reduction of Discrete-Event Systems

Abstract

In the supervisory control theory of discrete event systems, since the supremal supervisor incorporates transition constrains of both the plant and the specification, the state size of the supervisor is usually large and the control logic is difficult to understand. Thus, computing for reduced supervisors with small sizes is meaningful both for designing and implementation. We propose an algorithm that a reduced supervisor can be separated from the supremal supervisor if a sufficient condition is satisfied. The algorithm for checking the sufficient condition is also presented. In the case that the sufficient condition is satisfied, a reduced supervisor can be computed in a complexity of O(m.n), where the integers m and n are the state number of the supremal supervisor and the cardinality of the event set, respectively. And the state size of the reduced supervisor is equal or less than that of the specification. Some examples are presented to illustrate the proposed approach.

This work was supported in part by the National Natural Science Foundation of China under Grant 61966008, National Natural Science Foundation of GuangXi Province, China under Grant Nos. 2018GXNSFAA294052, 2020GXNSFBA159069 and 2019JJA170060, Guangxi Science and Technology Planning Project Grant No. AB18126063, Guangxi Key Laboratory of Trusted Software (Nokx201926), and Young and Middle-aged Scientific Research Basic Ability Promotion Project of Guangxi under Grant No. 2020KY02031.