Notes on Supervisory Control of Fuzzy Discrete Event Systems

Abstract

Since the supervisory control of fuzzy discrete event systems (fuzzy DESs) was established in 2005, there have been meaningful development. The main contributions of the paper include two points: First we establish another supervisory control theorem of fuzzy DES. Here our purpose is to achieve the objective set (specifications) K~ (instead of its prefix-closure language), and we use two supervisors to control the fuzzy DES, and K~ can be between the controlled languages generated by the two supervisors. Also, a test algorithm is described to check whether or not the fuzzy controllability condition holds. Second, we further show two fundamental properties of the largest fuzzy sublanguage and the s-mallest prefix-closed fuzzy controllable superlanguage of a given fuzzy language, and two equivalence characterizations of the largest fuzzy sublanguage and the smallest prefix-closed fuzzy controllable superlanguage are given.