Maximally permissive mutually and globally nonblocking supervision with application to switching control

Authors:
Ratnesh Kumar;Shigemasa Takai;Martin Fabian;Toshimitsu Ushio
Affiliations:
Department of Electrical and Computer Engineering, Iowa State University, Ames, IA 50014, USA;Department of Electronics and Information Science, Kyoto Institute of Technology, Sakyo-ku, Kyoto 606-8585, Japan;Department of Signals and Systems, Chalmers University of Technology, SE-412 96 Göteborg, Sweden;Department of Systems Innovation, Osaka University, Toyonaka, Osaka 560-8531, Japan
Venue:
Automatica (Journal of IFAC)
Year:
2005

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Abstract

A supervisor is said to be mutually nonblocking with respect to a pair of specifications if upon completing a task in any of the specifications, it can continue on to complete the task in the other specification, i.e., the two specifications do not block each other. The notion of mutually nonblocking supervisor was introduced in Fabian and Kumar [2000. Automatica, 36(12), 1863-1869]. In this paper, we present an algorithm of polynomial complexity for computing a maximally permissive mutually and globally nonblocking supervisor. In case such a supervisor does not exist, we present a technique for relaxing the specifications for which a supervisor exists. The algorithms are based on a notion of attractability, and as a special case offer a new way of computing the maximally permissive nonblocking supervisors. The results are then applied to design of maximally permissive switching supervisors so as to allow for switching between the specifications at any time while the system is executing.