Liveness-enforcing Supervision Research Articles

On the state liveness of some classes of guidepath-based transport systems and its computational complexity

Guidepath-based transport systems is a pertinent abstraction for the traffic that is generated in many contemporary applications, ranging from industrial material handling and robotics, to computer game animations and the qubit transport systems employed in quantum computing. A particular problem that must be effectively addressed for the systematic operation of these systems, is the preservation of their “liveness”, i.e., the preservation of the ability of the system agents to complete their current assignments and engage successfully in similar assignments in the future operation of the system. This paper provides a systematic and comprehensive characterization of the notion of “liveness” for the entire spectrum of the aforementioned transport systems, and it further investigates the implications of this characterization for the deployment of maximally permissive liveness-enforcing supervision for the underlying traffic. It is shown that the computational complexity of the sought supervisors is contingent upon certain structural and operational attributes of the considered transport systems, that define, thus, a useful taxonomy for these environments. The paper proposes effective and efficient liveness-enforcing supervisors for each member of this taxonomy. Furthermore, the concluding part of the paper indicates how the obtained results can be integrated in a broader control framework for the considered transport systems that will also address time-related performance considerations for these environments, like the maximization of their throughput.

Throughput Maximization of Capacitated Re-Entrant Lines Through Fluid Relaxation

This paper extends the scheduling methodology for complex stochastic networks that is based on the solution of a “fluid” relaxation (FR) at each decision point of the original scheduling problem to stochastic networks with blocking and deadlocking effects. For a clearer and more concrete treatment, the presented results are developed in the operational context of a re-entrant line (RL) with finite buffering capacity at each workstation; these RLs are characterized as “capacitated RLs (CRLs).” From a methodological standpoint, the paper results are enabled by a pre-established ability to control the underlying resource allocation for deadlock freedom and by the further ability to express the corresponding deadlock avoidance policy as a set of linear inequalities on the system state. Also, the employed FR for this new regime differs from the FRs that have been employed in past implementations of the method since it must account for the blocking effects that take place in the considered CRLs. The efficacy of the presented scheduling method is assessed through numerical experimentation that compares, for a set of “benchmark” CRLs, the performance of the scheduling policies obtained through this method to 1) the performance of the corresponding optimal scheduling policies and also to 2) the performance of some other heuristic scheduling policies for these systems that are adapted from the relevant literature. Finally, an additional set of experiments demonstrates and assesses the scalability of the presented method by applying it to some pretty large system configurations. Note to Practitioners —While the real-time management/scheduling of complex resource allocation systems (RASs) is a thriving area in general, the particular problem of scheduling such systems with extensive blocking and deadlocking effects in their operation has received very limited attention. To a large extent, this is due to the fact that the effective scheduling of this particular RAS class requires the initial resolution of an additional problem, of a more combinatorial type, that concerns the establishment of “liveness” for the underlying workflow, i.e., the ability of all the activated jobs to proceed to their completion securing successfully all the required resources for the execution of their various processing stages, and avoiding the formation of any deadlocks or livelocks. On the other hand, this problem of liveness enforcement for the considered RAS has received extensive attention within a certain part of the controls community during the past decades, and the currently available results provide a broad range of methods and policies for supporting the necessary supervision. This paper combines the aforementioned results on the RAS liveness-enforcing supervision with a scheduling methodology that has been very popular in the context of other hard scheduling problems in order to develop a complete scheduling methodology for the considered RAS. Extensive numerical experimentation reported in this paper demonstrates and assesses the efficacy of the presented method. Finally, in an effort to provide more concrete and simpler exposition for the presented developments, the results are presented in the operational context of a “capacitated re-entrant line (CRL),” i.e., a particular RAS class modeling the operation of RLs with finite buffering capacity at its various workstations.

Liveness-Enforcing Supervision in AMS-Oriented HAMGs: An Approach Based on New Characterization of Siphons Using Petri Nets

In the context of automated manufacturing systems, flexibility and synchronization are two main representative formations. Supervisory control techniques for flexibility have gained increasing attention, but those for synchronization operations have received little notice. Based on their comparison, our work makes threefold contributions. First, we propose a novel characterization of siphons, i.e., type I and type II, based on a special kind of Petri nets, namely, hierarchical augmented marked graphs (HAMGs), which integrate multilevel synchronization into a system. This characterization of siphons is further proved to be a crucial and essential description for both synchronization and flexibility. Second, event circular-wait is proposed to describe the occurrence of deadlocks in HAMGs. Its counterpart is resource circular-wait in flexibility. Ours is a more general and accurate characterization of deadlocks. The liveness of HAMGs can be attributed to the absence of undermarked siphons. Third, a unified liveness-enforcing supervisory control is established based on new characterization of siphons with the aid of generalized mutual exclusion constraints. Supervisor simplification based on inequality analysis is provided for structure simplicity. An experimental study illustrates the correctness of such characterization and the effectiveness of our proposed control method.

Maximally permissive deadlock avoidance for resource allocation systems with R/W-locks

This paper extends the existing theory on maximally permissive liveness-enforcing supervision of resource allocation systems (RAS) so that it can handle RAS with reader / writer (R/W-) locks. A key...

Maximally Permissive Deadlock Avoidance for Resource Allocation Systems with R/W-Locks

This paper extends the existing theory on maximally permissive liveness-enforcing supervision of resource allocation systems (RAS) so that it can handle RAS with reader/writer (R/W-) locks. A key challenge that is posed by this new RAS class stems from the fact that the underlying state space is not necessarily finite. We effectively address this obstacle by taking advantage of special structure that exists in the set of inadmissible states and enables a finite representation of this set through its minimal elements.

A Practical Approach for Maximally Permissive Liveness-Enforcing Supervision of Complex Resource Allocation Systems

Past works towards the effective deployment of the maximally permissive liveness-enforcing supervisor (LES) for sequential resource allocation systems (RAS) have been stalled by: (i) the NP-Hardness of the computation of this policy for the majority of the considered RAS classes and (ii) the inability of the adopted more compact representations of the underlying RAS dynamics to provide an effective representation of the target policy for all RAS instantiations. This paper proposes a novel approach to the aforementioned problem, that can be perceived as a two-stage process: The first stage computes the maximally permissive LES by employing an automaton-based representation of the RAS behavior and techniques borrowed from the Ramadge & Wonham (R&W) Supervisory Control framework. The second stage seeks the development of a more compact representation for the dichotomy into admissible and inadmissible-or “safe” and “unsafe”-subspaces of the RAS state space, that is effected by the LES developed in the first stage. This compact representation is obtained by: (i) taking advantage of certain properties of the underlying subspaces and (ii) the employment of pertinent data structures. The resulting approach is also “complete,” i.e., it will return an effectively implementable LES for any given RAS instantiation. Numerical experimentation demonstrates the efficacy of the approach and establishes its ability to support the deployment of maximally permissive LES for RAS with very large structure and state spaces.

Supervisor Design to Enforce Production Ratio and Absence of Deadlock in Automated Manufacturing Systems

This paper proposes a new Petri net class, namely, Ratio-enforced weighted Augmented Marked Graphs (RAMGs), and solves ratio control and liveness-enforcing supervision problems for automated manufacturing systems. RAMGs can ensure the required product ratios as demanded by production planners. Since the deadlock of such a system can be attributed to improper acquisition of finite shared resources, a supervisor is introduced such that they are properly allocated. This paper proves that ratio and supervisory controllers for an RAMG can be separately designed. Their design methods are presented. Examples are given to illustrate them.

On the Complexity of Maximally Permissive Deadlock Avoidance in Multi-Vehicle Traffic Systems

The establishment of collision-free and live vehicle motion is a prominent problem for many traffic systems. Past work studying this problem in the context of guidepath-based and free-range vehicular systems has implicitly assumed that its resolution through maximally permissive supervision is NP-hard, and therefore, it has typically pursued suboptimal (i.e., more restrictive) solutions. The work presented in this technical note offers formal proof to this implicit assumption, closing the apparent gap in the existing literature. In the process, it also derives an alternative proof for the NP-hardness of maximally permissive liveness-enforcing supervision in Linear, Single-Unit Resource Allocation Systems, that is more concise and more lucid than the currently existing proof.

The thinning problem†

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 behaviours while optimizing some performance criterion. A canonical characterization of this problem is provided in the form of a mixed integer programming 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 development of the article, examples are used to highlight the concepts and formulations involved.

Implicit Siphon Control and Its Role in the Liveness-Enforcing Supervision of Sequential Resource Allocation Systems

The work presented in this paper seeks 1) to correct and generalize some previously published results regarding the siphon control in PT-ordinary Petri nets (PNs) and, subsequently, 2) to employ this generalized framework in order to provide an alternative explanation of the way in which certain methodologies that have been proposed in the past enforce the liveness of a particular class of PT-ordinary PN-modeling resource allocation. The derived characterizations provide a unifying framework for analyzing and interpreting the aforementioned methodologies, and also, they reveal that approaches that have been considered as disparate in the current literature can actually be "mixed" toward the development of an ever richer set of liveness-enforcing supervisory-control policies for the considered class of PNs

Liveness-enforcing supervision of bounded ordinary Petri nets using partial order methods

This paper combines and refines recent results into a systematic way to verify and enforce the liveness of bounded ordinary Petri nets. The approach we propose is based on a partial-order method called network unfolding. Network unfolding maps the original Petri net to an acyclic occurrence net. A finite prefix of the occurrence net is defined to give a compact representation of the original net reachability graph while preserving the causality between net transitions. A set of transition invariants denoted as base configurations is identified in the finite prefix. These base configurations capture all of the fundamental executions of the net system, thereby providing a modular way to verify and synthesize supervisory net systems. This paper proves necessary and sufficient conditions that characterize the original net liveness and the existence of maximally permissive supervisory policies that enforce liveness.

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.

Liveness-Enforcing Supervision for n-Safe Ordinary Petri Nets with Uncontrollable Transitions

This paper presents necessary and sufficient conditions that verify the existence of liveness-enforcing supervisory policies for n-safe ordinary Petri nets with uncontrollable transitions. The approach is based on a partial method called network unfolding, which unfolds the original net to an acyclic occurrence net. The occurrence net preserves the ordering relationship among transitions and enumerates all the reachable markings of the original network. We identify a set of base configurations from the occurrence net. A base configuration may be live or deadlocked. A set of base configurations may be in cyclic lock. We prove that there exists a liveness-enforcing supervisory policy if and only if every transition of the original net is contained in some live base configuration and every deadlocked base configuration as well as every cyclic lock is controllable. Furthermore, we show that the liveness-enforcing supervisory policy constructed in the sufficiency proof is maximally permissive (or minimally restrictive).