Robust Deadlock Avoidance for Sequential Resource Allocation Systems With Resource Outages

Abstract

While the supervisory control (SC) problem of (maximally permissive) deadlock avoidance for sequential resource allocation systems (RASs) has been extensively studied in the literature, the corresponding results that are able to address potential resource outages are quite limited, both, in terms of their volume and their control capability. This paper leverages the recently developed SC theory for switched discrete event systems (s-DES) in order to provide a novel systematic treatment of this more complicated version of the RAS deadlock avoidance problem. Following the modeling paradigm of s-DES, both the operation of the considered RAS and the corresponding maximally permissive SC policy are decomposed over a number of operational modes that are defined by the running sets of the failing resources. In particular, the target supervisor must be decomposed to a set of “localized predicates,” where each predicate is associated with one of the operational modes. A significant part, and a primary contribution, of this paper concerns the development of these localized predicates that will enable the formal characterization and the effective computation of the sought supervisor. With these predicates available, a distributed representation for the sought supervisor that is appropriate for real-time implementation is eventually obtained through an adaptation of the relevant distributed algorithm that is provided by the current s-DES SC theory.