Marian V. Iordache

Synthesis of deadlock prevention supervisors using Petri nets

Given an arbitrary Petri net (PN) structure, which may have uncontrollable and unobservable transitions, the deadlock prevention procedure presented here determines a set of linear inequalities on the PN markings. When the PN is supervised so that its markings satisfy these inequalities, the supervised net is proved to be deadlock-free for all initial markings that satisfy the supervision constraints. Deadlock-freedom implies that there will always be at least one transition that is enabled in the closed-loop (supervised) system. The method is not guaranteed to ensure liveness, as it can be applied to systems that cannot be made live under any circumstances. However, for controllable and observable PNs, it is shown that, when the method ensures liveness as well, the liveness-ensuring supervisor is least restrictive. Moreover, it is shown that the method is not restrictive even for PNs in which not all transitions can be made live. The procedure allows automated synthesis of the supervisors.

Supervision Based on Place Invariants: A Survey

The supervision based on place invariants (SBPI) is an efficient technique for the supervisory control of Petri nets. This paper reveals the significance of the SBPI based on a literature survey, applications, and an analysis of problems and supervisory settings that can be addressed using SBPI. Special attention is given to the various settings within which the problem can be formulated. Such settings can be distinguished based on the concurrency type, the type of controllability and observability, and the centralized or decentralized type of supervision. As we show, it is possible to approach the most general settings in a purely structural way, without resorting to reachability analysis. We begin by describing the SBPI problem and the literature methods that address this problem or are related to it. Then, we proceed to show classes of problems that can be reduced to the SBPI problem. In the SBPI, the specification is described as a system of inequalities that the Petri net marking must satisfy at any time. However, as we show, problems involving more general specifications can be approached in the SBPI setting, sometimes under additional assumptions, by performing net and/or specification transformations. Four of the specifications we will consider are logic constraints, language specifications, disjunctions of linear constraints, and liveness. We conclude with a presentation of possible applications of the SBPI approach to programming with semaphores, fault tolerance, and synchronic-distance based designs.

Synthesis of supervisors enforcing general linear constraints in Petri nets

Efficient techniques exist for the design of supervisors enforcing constraints consisting of linear marking inequalities. This note shows that without losing the benefits of the prior techniques, the class of constraints can be generalized to linear constraints containing marking terms, firing vector terms, and Parikh vector terms. We show that this extended class of constraints is more expressive. Furthermore, we show that the extended constraints can describe any supervisor consisting of control places arbitrarily connected to the transitions of a plant Petri net (PN). The supervisor design procedure we propose is as follows. For PNs without uncontrollable and unobservable transitions, a direct method for the design of a PN supervisor that is least restrictive is given. For PNs with uncontrollable and/or unobservable transitions, we reduce the problem to the design of supervisors enforcing linear marking inequalities.

A method for the synthesis of liveness enforcing supervisors in Petri nets

Given an arbitrary Petri net structure, which may have uncontrollable and unobservable transitions and may be unbounded, the procedure described in this paper generates a supervisor for liveness enforcement. The supervisor is specified as a conjunction of linear marking inequalities. For all initial markings satisfying the linear marking inequalities, the supervised Petri net is live. Moreover, the supervision is least restrictive in the fully controllable and observable case.

Design of T-liveness enforcing supervisors in Petri nets

This paper presents a procedure for the design of supervisors that enforce the transitions in a given set T to be live. T-liveness enforcement corresponds to full liveness enforcement when T equals the total set of transitions. Rather than assuming a given initial marking, this procedure generates at every iteration a convex set of admissible initial markings. In the case of full liveness enforcement and under certain conditions also in the case of T-liveness enforcement, the convex set of each iteration includes the set of markings for which liveness/T-liveness can be enforced. When the procedure terminates, and if it terminates, the final convex set contains only markings for which T-liveness can be enforced. Then, the supervisor keeping the Petri net (PN) marking in this convex set can be easily designed using the place invariant based approach. This paper focuses on the fully controllable and observable PNs. Several extensions of the procedure, including to partially controllable and observable PNs, are outlined.

Decentralized supervision of Petri nets

This note extends previous results on the supervision of Petri nets (PNs) to the decentralized setting. While focusing on the extension of supervision based on place invariants (SBPI), the proposed approach is more general and could be applied to other types of supervision as well. We begin by introducing d-admissibility as an extension to the decentralized setting of the centralized admissibility concept. We define also structural d-admissibility, as the counterpart of the simple sufficient conditions for centralized admissibility in the context of the SBPI. Note that (structural) d-admissibility is only sufficient for a specification to be enforcible with the same permissiveness as in the centralized setting with full controllability and observability. However, structural d-admissibility can be checked with low polynomial complexity. Based on the d-admissibility concept, we propose two suboptimal methods to design decentralized supervisors. The first method is to find a centralized solution, and then distribute the centralized supervisory policy by means of communication. The amount of communication can be minimized by means of an integer linear program (ILP). The second method is to transform the specification to a (more restrictive) d-admissible specification by means of an ILP. In the case of decentralized supervision with communication, the ILP can be used to minimize the amount of communication required by the solution.

Synthesis of supervisors enforcing general linear vector constraints in Petri nets

Considers the problem of enforcing linear constraints containing marking terms, firing vector terms, and Parikh vector terms. Such constraints increase the expressivity power of the linear marking constraints. We show how this new type of constraints can be enforced in Petri nets. In the case of fully controllable and observable Petri nets, we give the construction of a supervisor enforcing such constraints. In the case of Petri nets with uncontrollable and/or unobservable transitions, we reduce the supervisor synthesis problem to enforcing linear marking constraints on a transformed Petri net.

Petri nets and programming: A survey

Petri nets and related models have been used for specification, analysis, and synthesis of programs. The paper contains a survey of several literature approaches and an examination of their relationship to Petri net modeling and supervisory control. The discussion is restricted to Petri net models in the class of place/transitions nets and the supervisory control of this class of models.

Petri Net Supervisors for Disjunctive Constraints

The paper presents an approach for the design of supervisors for disjunctive constraints in which the supervisors are represented by labeled Petri nets. This approach extends our previous results in two ways. First, the supervisors are now guaranteed to be least restrictive. Second, the constraints may now also include the firing vector. The approach is illustrated on the readers/writers problem. While the results are obtained in the fully controllable and observable setting, issues arising when the system is partially controllable and partially observable are also discussed. The approach is developed under certain boundedness assumptions.

Concurrent program synthesis based on supervisory control

The paper introduces a new area of application of the supervisory control (SC) methods and a project dealing with this research topic. Based on the observation that various constraints on the operation and synchronization of concurrent processes can be expressed in terms of SC specifications, the paper proposes the application of SC to the automation of concurrent program synthesis. Specifically, the paper proposes a three-stage approach allowing to generate automatically the part of the programs that deals with the coordination of concurrent processes. In a first stage, Petri net models are extracted from a high level specification. An SC specification is also extracted. Then, SC is applied to generate the supervisor enforcing the specification. Finally, the programs representing the processes and the supervisor are generated. This work is motivated by the difficulty of writing correctly concurrent programs. Since this difficulty is due to the constraints on the operation and synchronization of concurrent processes, research in this area has the potential of simplifying the development of concurrent programs.