Abstraction Based Supervisory Control for Non-Regular -Languages∗. Issue 28 (2022)

• Record Type: Journal Article
• Authors: Triska, Lukas; Moor, Thomas
• Is Part Of: IFAC-PapersOnLine. Volume 55:Issue 28(2022)
• Page Start: 142
• Page End: 149
• Publication Date: 2022
• Subjects: supervisory control -- abstraction based controller design -- controllability prefix -- abstraction refinement -- unbounded Petri nets; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2022.10.336
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: The problem of supervisory control, in its most basic form, is well understood for regular parameters, i.e., with regular languages for plant and upper-bound language-inclusion specification. However, when dropping the requirement of regularity, the situation becomes much more involved: even decidability becomes an issue. In this paper, we propose a simplistic but yet fairly general approach in that non-regular parameters are replaced by regular substitutes. In a language based setting we provide (a) conditions such that any solution found for the substitute parameters carries over to the original problem and (b) a refinement scheme which can be applied when the substitute parameters render the control problem at hand unsolvable. For practical purposes, we further elaborate our approach for plants represented as unbounded Petri nets and (c) identify a condition under which the alternation of trial synthesis and refinement is guaranteed to terminate with success.