Liveness-enforcing supervision for resource allocation systems with uncontrollable behavior and forbidden states

Although liveness enforcing supervision (LES) of sequential resource allocation systems (RAS) is currently a well-established problem in the Discrete Event System literature, all prior work on it has addressed the underlying LES synthesis problem under the assumption that the system behavior is totally controllable. The work presented in this paper seeks to develop correct and scaleable LES for RAS that present uncontrollability with respect to: 1) the timing of some requested resource allocations, i.e., these allocations will take place as long as the requested resources are available and/or 2) the routing of certain job instances that, after some processing stages, might request special treatment or rework. In addition, the last part of the paper addresses the accommodation in the original LES synthesis problem of externally imposed logical constraints, that constitute "forbidden state" specifications and possess a linear characterization with respect to the system resource allocation state. All problems are addressed in the context of Conjunctive/Disjunctive (CD)-RAS, that constitutes one of the broadest RAS classes. investigated in the literature, allowing for arbitrarily structured resource allocations associated with the various process stages, and process routing flexibility.