Liveness-enforcing supervision of sequential resource allocation systems is currently a well-defined problem, underlying the operation of many contemporary technological systems, spanning a wide spectrum of applications. This technical note provides a brief overview of the currently available results, delineating, both, our major analytical understandings/characterizations concerning the problem concepts/structure and its complexity, and also, our ability to synthesize effective and computationally tractable solutions to it. The last part of the document identifies open / unaddressed research issues, the resolution of which will extent the power of the current theory and will allow the integration of the developed results in the broader control frameworks managing the behavior of these environments.

The need for e#ective and e#cient deadlock avoidance policies (DAP's) is ever increasing due to the higher demand for system automation. This paper considers the deadlock avoidance problem for the class of Conjunctive/Disjunctive (sequential) resource allocation systems (C/D-RAS), in which multiple resource acquisitions and flexible routings are allowed. A new siphon-based characterization of deadlocks arising in C/D-RAS is developed, and subsequently, this characterization facilitates the development of a polynomial complexity deadlock avoidance policy for the considered RAS class. The developed policy can be perceived as a generalization of RUN DAP, originally developed for sequential RAS with unit resource allocations and no routing flexibility. The proposed approach is demonstrated by an example. 1. Introduction Deadlock avoidance in (sequential) resource allocation systems (S-RAS) is a well-defined problem in Discrete Event System literature. From a theoretical standpoint, the pr...

As many contemporary technological applications move to operational modes of more extensive and flexible automation, there is a rising need to design and control the underlying resource allocation not only for efficiency, but also for logical correctness and internal consistency. The material presented in this chapter offers a unifying and comprehensive treatment of a class of policies that have been proposed as an effective and efficient solution to this emerging class of logical control problems. 1

Development and maintenance of control software has emerged as one of the most difficult problems associated with building Flexible Manufacturing Systems (FMS). FMS controllers , potentially the most flexible FMS components, are characterized by their inflexibility. To support configuration flexibility of FMS controllers, this work proposes a modular hierarchical control structure which combines multiple interacting models of the FMS. High resolution computational models which encode system state transition information are used for the lowest level of control. Given the FMS state, these models identify the set of enabled state transitions. At a higher level of abstraction, structural models which elucidate system structural characteristics are used to implement Structural Control Policies, SCP's,. These policies partition the set of enabled state transitions into feasible and infeasible transitions based on deadlock considerations. Issues in the development of SCP's include correctness...

The main problem addressed in this work is how to confine the set of sequential processes of a disjunctive / conjunctive resource allocation system (D/C-RAS) to a subset of their feasible behaviors while optimizing some performance criterion. We provide a canonical characterization of this problem in the form of a Mixed Integer Programming (MIP) formulation, for the case that the optimized performance criterion is the maximization of the system throughput. However, an important additional development of this effort is a complete analytical characterization of the performance control problem of D/C-RAS. This characterization is based on an effective integration of recent results on the liveness-enforcing supervision of D/C-RAS with the theory of Markov Decision Processes, and it concretizes the interaction between the D/C-RAS logical and performance control. Throughout the paper development, a small example highlights the involved concepts and formulations.

Abstract — Generalized algebraic deadlock avoidance policies (DAPs) for sequential resource allocation systems (RAS) have recently been proposed as an interesting extension of the class of algebraic DAPs, that maintains the analytical representation and computational simplicity of the latter, while it guarantees completeness with respect to the maximally permissive DAP. The original work of [1] that introduced these policies also provided a design methodology for them, but this methodology is limited by the fact that it necessitates the deployment of the entire state space of the considered RAS. Hence, this paper seeks the development of an alternative computational tool that can support the synthesis of correct generalized algebraic DAPs while controlling the underlying computational complexity. More specifically, the presented correctness verification test possesses