Robust Deadlock Avoidance for Sequential Resource Allocation Systems With Resource Outages

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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. Note to Practitioners —This paper extends the existing theory of deadlock avoidance for buffer-space allocation in flexibly automated production systems so that it accounts for disruptive effects due to potential temporary outages of some of the system servers. The set of the failing servers at any time instant defines the corresponding operational mode for the underlying resource allocation system. The primary problem that is addressed by this paper is the synthesis of a resource allocation policy that will ensure the ability of all process instances that do not require the failing resources in a particular mode, to execute repetitively and complete successfully while the system remains in that mode. In line with some past literature on this problem, we call the corresponding supervisory control problem as “robust deadlock avoidance,” and we leverage results from the recently emerged theory for modeling and control of switched discrete event systems in order to characterize and compute a maximally permissive solution for it.