Zhennan Fei

Modeling sequential resource allocation systems using Extended Finite Automata

Deadlock avoidance for resource allocation systems (RAS) is a well-established problem in the Discrete Event System (DES) literature. This paper is mainly concerned with modeling the class of Conjunctive / Disjunctive sequential resource allocation systems (C/D RAS) as finite automata extended with variables. The proposed modeling approach allows for modeling multiple instance execution, routing flexibility and failure handling. With an appropriate model of the system, a symbolic approach is then used to synthesize the optimal supervisor, in the least restrictive sense. Furthermore, a set of compact logical formulae can be extracted and attached to the original model, which results in a modular and comprehensible representation of the supervisor

A BDD-Based Approach for Designing Maximally Permissive Deadlock Avoidance Policies for Complex Resource Allocation Systems

In order to develop a computationally efficient implementation of the maximally permissive deadlock avoidance policy (DAP) for complex resource allocation systems (RAS), a recent approach focuses on the identification of a set of critical states of the underlying RAS state-space, referred to as minimal boundary unsafe states. The availability of this information enables an expedient one-step-lookahead scheme that prevents the RAS from reaching outside its safe region. The work presented in this paper seeks to develop a symbolic approach, based on binary decision diagrams (BDDs), for efficiently retrieving the (minimal) boundary unsafe states from the underlying RAS state-space. The presented results clearly demonstrate that symbolic computation enables the deployment of the maximally permissive DAP for complex RAS with very large structure and state-spaces with limited time and memory requirements. Furthermore, the involved computational costs are substantially reduced through the pertinent exploitation of the special structure that exists in the considered problem. Note to Practitioners-A key component of the real-time control of many flexibly automated operations is the management of the allocation of a finite set of reusable resources among a set of concurrently executing processes so that this allocation remains deadlock-free. The corresponding problem is known as deadlock avoidance, and its resolution in a way that retains the sought operational flexibilities has been a challenging problem due to: (i) the inability to easily foresee the longer-term implications of an imminent allocation and (ii) the very large sizes of the relevant state spaces that prevent an online assessment of these implications through exhaustive enumeration. A recent methodology has sought to address these complications through the offline identification and storage of a set of critical states in the underlying state space that renders efficient the safety assessment of any given resource allocation. The results presented in this paper further extend and strengthen this methodology by complementing it with techniques borrowed from the area of symbolic computation; these techniques enable a more compressed representation of the underlying state spaces and of the various subsets and operations that are involved in the pursued computation.

Supervisory Control for State-Vector Transition Models—A Unified Approach

A generic state-vector transition (SVT) model is suggested, including a flexible synchronous composition involving both shared variables and events. This model is analyzed, focusing on properties that are important for supervisor synthesis. A synthesis procedure is then developed for the SVT model, where supervisor guards are generated that guarantee a controllable, nonblocking and maximally permissive supervisor. Novel conditions are introduced, such that more flexible specifications can be applied than earlier suggested for related models. Since the SVT model includes automata and (colored) Petri nets, optionally extended with variables, guards and actions, as special cases, the suggested synthesis approach unifies supervisor synthesis for the main discrete event model classes. Finally, the SVT model is naturally represented and efficiently computed based on binary decision diagrams, and the resulting supervisor guards are easily implemented in industrial control systems.

Symbolic reachability computation using the disjunctive partitioning technique in Supervisory Control Theory

Supervisory Control Theory (SCT) is a model-based framework for automatically synthesizing a supervisor that minimally restricts the behavior of a plant such that a given specification is fulfilled. A problem, which prevents SCT from having a major breakthrough industrially, is that the supervisory synthesis often suffers from the state-space explosion problem. To alleviate this problem, a well-known strategy is to represent and explore the state-space symbolically by using Binary Decision Diagrams. Based on this principle, an efficient symbolic state-space traversal approach, depending on the disjunctive partitioning technique, is presented and the correctness of it is proved. Finally, the efficiency of the presented approach is demonstrated on a set of benchmark examples.

Invariant-based Supervisory Control of Switched Discrete Event Systems

This technical note introduces the notion of switched Discrete Event Systems (s-DES) and investigates its representational and computational potential in (i) the description and the analysis of the underlying DES behavior, (ii) the specification of the posed control requirements, and (iii) the eventual computation of the necessary control function. More specifically, it is shown that the potential decomposition of the overall DES behavior in a well defined set of “operational modes” enables the specification of control requirements and the synthesis of the corresponding control laws in a modular and distributed manner that takes full advantage of the aforementioned decomposition. The work is motivated by the need to cope with DES operating under a number of failing modes that result from non-catastrophic failures and repairs, and also DES that might evolve their operation through a number of “stages.” Furthermore, the technical developments of the technical note and their representational and computational power are further highlighted by an application example that is drawn from the area of robot pursuit on time-varying graphs; however, due to space considerations, this example is provided in an electronic supplement to the technical note.

Robust deadlock avoidance for sequential resource allocation systems with resource outages

While the problem of deadlock avoidance for sequential resource allocation systems (RAS) has been extensively studied in the literature, the current results that are able to address potential resource outages are pretty limited. In this work, we seek to extend the corresponding theory by leveraging and strengthening some recently developed results on the emergent theory of switched Discrete Event Systems.

Symbolic Supervisory Control of Timed Discrete Event Systems

We symbolically compute a nonblocking, controllable, and minimally restrictive supervisor for timed discrete event systems (TDESs), in the supervisory control theory context. We model TDES based on timed extended finite automata (TEFAs): an augmentation of extended finite automata (EFAs) by incorporating discrete time into the model. EFAs are ordinary automata extended with discrete variables, where conditional expressions and update functions can be attached to the transitions. The controllability is defined based on the corresponding tick models of the TEFAs. A tick can be considered as an event that is generated by a global digital clock. The tick models suffer from a major problem: the state size is very sensitive to the clock frequency. We show how a controllable supervisor, equivalent to the one computed based on the tick models, can be obtained by eliminating the tick events. To tackle large problems, all computations are conducted symbolically using binary decision diagrams (BDDs). We show that, based on the proposed approach, a fixed point is reached earlier in the reachability analysis and that the size of the intermediate BDDs usually becomes smaller. The framework has been applied to a real industrial application and several benchmarks.

Symbolic computation and representation of deadlock avoidance policies for complex resource allocation systems with application to multithreaded software

In our recent work, we proposed a series of binary decision diagram (BDD-) based approaches for developing the maximally permissive deadlock avoidance policy (DAP) for a class of complex resource allocation systems (RAS). In this paper, (i) we extend these approaches by introducing a procedure that generates a set of comprehensible “guard” predicates to represent the resulting DAP, and (ii) we customize them to the problem of deadlock avoidance in shared-memory multithreaded software, that has been previously addressed by the Gadara project. In the context of this last application, the generated guards can be instrumented directly into the source code of the underlying software threads, providing, thus, a very efficient and natural representation of the target policy. At the same time, by integrating the representational and computational strengths of symbolic computation, the presented approach can support the computation of the maximally permissive DAP for RAS corresponding to problem instances of even larger scale and complexity than those addressed in the current literature.

A Symbolic Approach for Maximally Permissive Deadlock Avoidance in Complex Resource Allocation Systems

To develop an efficient implementation of the maximally permissive deadlock avoidance policy (DAP) for complex resource allocation systems (RAS), a recent approach focuses on the identification of a set of critical states of the underlying RAS state-space, referred to as minimal boundary unsafe states. The availability of this information enables an expedient one-step-lookahead scheme that prevents the RAS from reaching outside its safe region. This paper presents a symbolic approach that provides those critical states. Furthermore, by taking advantage of certain structural properties regarding RAS safety, the presented method avoids the complete exploration of the underlying RAS state-space. Numerical experimentation demonstrates the efficiency of the approach for developing the maximally permissive DAP for complex RAS with large structure and state-spaces, and its potential advantage over similar approaches that employ more conventional representational and computational methods.

Symbolic computation of nonblocking control function for timed discrete event systems

In this paper, we symbolically compute a minimally restrictive nonblocking supervisor for timed discrete event systems, in the supervisory control theory context. The method is based on Timed Extended Finite Automata, which is an augmentation of extended finite automata (EFAs) by incorporating discrete time into the model. EFAs are ordinary automaton extended with discrete variables, guard expressions and action functions. To tackle large problems all computations are based on binary decision diagrams (BDDs). The main feature of this approach is that the BDD-based fixed-point computations is not based on “tick” models that have been commonly used in this area, leading to better performance in many cases. As a case study, we effectively computed the minimally restrictive nonblocking supervisor for a well-known production cell.