On Supervisory Policies that Enforce Global Fairness and Bounded Fairness in Partially Controlled Petri Nets

In this paper we consider the notions of global-fairness (G-fairness) and bounded-fairness (B-fairness) for arbitrary Petri nets (PNs). G-fairness in a PN guarantees every transition occurs infinitely often in every valid firing sequence of infinite length. B-fairness guarantees a bound on the number of times a transition in the PN can fire without some transition firing at least once. These properties are guaranteed without recourse to assumptions on firing time distributions or contention resolution policies. We present a necessary and sufficient condition for the existence of supervisory policies that enforce G-fairness and B-fairness along with various observations on the closure properties of policies that enforce these notions of fairness in controlled PNs with a (possibly) non-empty set of uncontrollable transitions. We also derive a necessary and sufficient condition that guarantees a minimally restrictive supervisor that enforces these notions of fairness for bounded PNs. These results are illustrated via examples.     

On supervisory policies that enforce liveness in completelycontrolled Petri nets with directed cut-places and cut-transitions

The process of synthesizing a supervisory policy that enforces liveness in a Petri net (PN), where each transition can be prevented from firing by an external agent, can be computationally burdensome in general. We consider PNs that have a directed cut place or a cut-transition. A place (transition) in a connected PN is said to be a cut place (cut-transition) if its removal will result in two disconnected component PNs. A cut place is said to be a directed cut-place, if in the original PN, all arcs into this cut place emanate from transitions in only one of the two disconnected component PNs. The authors show there is a supervisory policy that enforces liveness in the original PN if and only if similar policies exist for two PNs derived from the disconnected components obtained after the removal of the directed cut-place (cut-transition). The utility of this observation in alleviating the computational burden of policy synthesis is illustrated via example     

Design of Optimal Petri Net Supervisors for Flexible Manufacturing Systems via Weighted Inhibitor Arcs

This paper develops an approach to the design of an optimal Petri net supervisor that enforces liveness to flexible manufacturing systems. The supervisor contains a set of observer places with weighted inhibitor arcs. An observer place with a weighted inhibitor arc is used to forbid a net from yielding an illegal marking by inhibiting the firing of a transition at a marking while ensuring that all legal markings are preserved. A marking reduction technique is presented to decrease the number of considered markings, which can dramatically lower the computational burden of the proposed approach. An integer linear program is presented to simplify the supervisory structure by minimizing the number of observer places. Finally, several examples are used to shed light on the proposed approach which can lead to an optimal supervisor for the net models that cannot be optimally controlled via pure Petri net supervisors.     

Some observations on supervisory policies that enforce liveness in partially controlled Free-Choice Petri nets

Every arc from a place to a transition in a Free-Choice Petri net (FCPN) is either the unique output arc of the place, or, the unique input arc to the transition [M.H.T. Hack, Analysis of production schemata by Petri nets, Master’s thesis, Massachusetts Institute of Technology, February 1972; W. Reisig, Petri Nets, Springer-Verlag, Berlin, 1985; T. Murata, Petri nets: properties, analysis and applications, Proc. IEEE 77 (4) (1989) 541–580]. We consider FCPNs that are not live [J.L. Peterson, Petri Net Theory and the Modeling of Systems, Prentice-Hall, Englewood Cliffs, NJ, 1981; W. Reisig, Petri Nets, Springer-Verlag, Berlin, 1985; T. Murata, Petri nets: properties, analysis and applications, Proc. IEEE 77 (4) (1989) 541–580], and we investigate the existence of supervisory policies that can enforce liveness in partially controlled FCPNs. The external agent, or supervisor, can only prevent the firing of some (i.e. not all) transitions in a partially controlled FCPN.

We first present an observation on supervisory policies that enforce liveness in partially-controlled FCPNs. Using this observation, we solve the supervisory synthesis problem for the family of c hoice-controlled FCPNs, defined in this paper. We then identify a new, sub-class of partially-controlled FCPNs that posses an easily-characterized (and easily-enforced) supervisory policy that enforces liveness.     

Polynomial synthesis of supervisor for partially observed discrete-event systems by allowing nondeterminism in control

We study the supervisory control of discrete-event systems (DESs) under partial observation using nondeterministic supervisors. We formally define a nondeterministic control policy and also a control & observation compatible nondeterministic state machine and prove their equivalence. The control action of a nondeterministic supervisor is chosen online, nondeterministically from among a set of choices determined offline. Also, the control action can be changed online nondeterministically (prior to any new observation) in accordance with choices determined offline. The online choices, once made, can be used to affect the set of control action choices in future. We show that when control is exercised using a nondeterministic supervisor, the specification language is required to satisfy a weaker notion of observability, which we define in terms of recognizability and achievability. Achievability serves as necessary and sufficient condition for the existence of a nondeterministic supervisor, and it is weaker than controllability and observability combined. When all events are controllable, achievability reduces to recognizability. We show that both existence, and synthesis of nondeterministic supervisors can be determined polynomially. (For deterministic supervisors, only existence can be determined polynomially.) Both achievability and recognizability are preserved under union, and also under intersection (when restricted over prefix-closed languages). Using the intersection closure property we derive a necessary and sufficient condition for the range control problem for the prefix-closed case. Unlike the deterministic supervisory setting where the complexity of existence is exponential, our existence condition is polynomially verifiable, and also a supervisor can be polynomially synthesized.     

On commoner's liveness theorem and supervisory policies that enforce liveness in free-choice Petri nets

A Petri net (PN) (Peterson, 1981; Reisig, 1985) is said to be live if it is possible to fire any transition from every reachable marking, although not necessarily immediately. A free-choice Petri net FCPN) is a PN, where every arch from a place to a transition is either the unique output arc from that place or it is the unique input arc to the transition. Commoner's Liveness Theorem (cf. Hack, 1972, Ch. 4; Reisig, 1985, Section 7.2) states that a FCPN is live if and only if every siphon contains a marked trap at the initial marking. A siphon (trap) is a collection of places P such that . We concern ourselves with marking-dependent supervisory policies that can prevent the firing of a transition. We characterize supervisory policies that enforce liveness in non-live FCPNs using observations that strongly parallel Commoner's Liveness Theorem. We use this characterization to establish the existence of supervisory policies that enforce liveness in a Class of FCPNs called independent, increasing free-choice petri nets (II-FCPNs).     

An Application of Independent, Increasing, Free-Choice Petri Nets to the Synthesis of Policies that Enforce Liveness in Arbitrary Petri Nets

The class of Independent, Increasing, Free-Choice Petri nets (II-FCPNs) was introduced in (Sreenivas, 1997c), where it is shown that any II-FCPN can be made live via supervision using a readily available policy. In a live Petri net (PN). Petri Net Theory and Modeling of systems. Prentice-Hall, Englewood Cliffs, NJ, Reisig (1985). Petri Nets. Springer, Berlin), it is possible to fire any transition from every reachable marking, although not necessarily immediately. In this paper we identify a class of PNs, where every transition is controllable, that are not necessarily II-FCPNs, that can be made live via supervision using a readily available policy constructed from the policy that enforces liveness in an II-FCPN.     

A Framework for Fault-Tolerant Control of Discrete Event Systems

We introduce a framework for fault-tolerant supervisory control of discrete-event systems. Given a plant, possessing both faulty and nonfaulty behavior, and a submodel for just the nonfaulty part, the goal of fault-tolerant supervisory control is to enforce a certain specification for the nonfaulty plant and another (perhaps more liberal) specification for the overall plant, and further to ensure that the plant recovers from any fault within a bounded delay so that following the recovery the system state is equivalent to a nonfaulty state (as if no fault ever happened). The specification for the overall plant is more liberal compared to the one for the nonfaulty part since a degraded performance may be allowed after a fault has occurred. We formulate this notion of fault-tolerant supervisory control and provide a necessary and sufficient condition for the existence of such a supervisor. The condition involves the usual notions of controllability, observability and relative-closure, together with the notion of stability. An example of a power system is provided to illustrate the framework. We also propose a weaker notion of fault-tolerance where following the recovery, the system state is simulated by some nonfaulty state, i.e., behaviors following the recovery are also the behaviors from some faulty state. Also, we formulate the corresponding notion of weakly fault-tolerant supervisory control and present a necessary and sufficient condition (involving the notion of language-stability) for the its existence. We also introduce the notion of nonuniformly-bounded fault-tolerance (and its weak version) where the delay-bound for recovery is not uniformly bounded over the set of faulty traces, and show that when the plant model has finitely many states, this more general notion of fault-tolerance coincides with the one in which the delay-bound for recovery is uniformly bounded.     

Supervisory control of discrete event systems with state-dependent controllability

This article studies the supervisory control problem of discrete event systems (DES) with state-dependent controllability. The new problem is given with the background of operating systems where the processes and the interrupt service routines (ISR) are supervised and coordinated. The new model is novel because the controllability of an event is changeable in the lifetime of system evolution, and dependent on the system state. Two fundamental problems are concerned with the new model: supervisor existence problem and supervisor synthesis problem. We derive a necessary and sufficient condition for the existence of the supervisor, and introduce an algorithm to synthesise the supremal supervisor in a given specification. With the background of process and ISR management in operating systems, some examples are given to show how the new model can be applied to practical computing.     

Supervisory control of partially observed discrete event systems with arbitrary control patterns

In this paper, we study supervisory control of partially observed discrete event systems with arbitrary control patterns. First, we present a necessary and sufficient condition for the existence of a supervisor for a given non-empty and closed language K. Next, we consider the case where the language K does not satisfy the condition. We prove that there always exists its infimal superlanguage for which there exists a supervisor when the set Gamma of control patterns is closed under intersection. This infimal superlanguage is the optimal solution larger than K. On the other hand, when Gamma is closed under union, there does not necessarily exist its supremal sublanguage for which there exists a supervisor. In other words, the optimal solution smaller than K does not exist in general. So, in this case, we present a suboptimal solution smaller than K.     

Closed-loop Live Marked Graphs under Generalized Mutual Exclusion Constraint Enforcement

Enforcing a supervisory control policy to avoid forbidden states on a discrete event system modeled by a Petri net may result in a non live system. This may happen even if the admissible states are specified by Generalized Mutual Exclusion Constraints (GMECs). This leads to the problem of synthesizing a maximally permissive control policy preserving liveness of the system under a GMEC. This problem is very interesting in practice, but difficult even for a restricted class of systems. In this paper, we focus on systems which can be modeled as live and safe Marked Graphs (MGs). On such systems, when some of the transitions are uncontrollable, a GMEC can be forced by a monitor place if a not maximally permissive policy is accepted, otherwise a more complex control has to be adopted. Anyway, liveness of the closed-loop system (plant plus control) is not guaranteed. Two sufficient conditions to verify the closed-loop liveness of a live and safe MG plant controlled by a monitor are derived. A sufficient condition for closed loop liveness of MGs where a GMEC has been enforced on is derived. In addition, a set of predicates is provided that enforces, in a maximally permissive way, a GMEC while preserving closed-loop liveness on live and safe MG systems under some restrictions.

Supervisory control of nondeterministic discrete-event systems with driven events via masked prioritized synchronization

Studies the supervisory control problem of nondeterministic discrete event systems with driven events in the setting of masked prioritized synchronous composition (MPSC). MPSC was extended from prioritized synchronous composition (PSC) by Kumar and Heymann (2000) in order to permit systems interaction with their environment via interface masks. They also studied the supervisory control problem under the assumption that the set of driven events was empty. In this paper, the aforementioned assumption is relaxed. We first derive relations among behaviors at different levels of the system. Next, we solve the supervisor synthesis problem for controlling the plant behavior as observed at the interface level. Finally, we give a necessary and sufficient condition for the existence of the supervisor for controlling the plant behavior as observed at the plant level. We establish a link between MPSC and PSC by showing that a supervisory control problem in the setting of MPSC can be transferred to a supervisory control problem in the setting of PSC under certain conditions.     

On asymptotically efficient solutions for a class of supervisorycontrol problems

We consider restricted sequences of forbidden-string and forbidden-state problems and show the limiting problem instance defined by a sequence has a solution if and only if each problem instance in the sequence has a solution. Furthermore, the supervisor that enforces the desired behavior in the limiting problem instance also enforces the desired behavior in each problem instance in the sequence. In essence, the storage requirement for supervisory control of each instance is bounded above by that of the limiting problem instance. In addition, if the limiting problem instance is available, a similar observation can be made regarding the complexity of supervisory control. This observation coupled with recent results on the solvability of the supervisory control problem involving certain classes of nonregular behaviors and finite-representations of infinite-state systems is suggested as an effective procedure to combat the computational and storage issues in supervisory control. We conclude with an incomplete list of future research directions     

扩展强化非对称选择网的活性和有界性

给出了一类非对称选择网(asymmetricchoicenet,简称AC网),扩展了强化非对称选择网结构活的充分必要条件,证明了扩展强化非对称选择网如果是结构活的,其标识的活性是可判定的.同时也证明了扩展强化非对称选择网活性的单调性,并给出其结构活和结构有界的充分必要条件.     

A deadlock prevention approach for a class of timed Petri nets using elementary siphons

To solve the problem of deadlock prevention for timed Petri nets, an effective deadlock prevention policy based on elementary siphons is proposed in this paper. Without enumerating reachable markings, deadlock prevention is achieved by adding monitors for elementary siphons, increasing control depth variables when necessary, and removing implicit, liveness‐restricted and redundant control places. The final supervisor is live. First, a timed Petri net is stretched into a stretched Petri net (SPN). Unchanging the system performance, each transition in the SPN has a unit delay time. Then the siphon‐control‐based approach is applied. Monitors computed according to the marking constraints are added to the SPN model to ensure all strict minimal siphons in the net invariant‐controlled. A liveness‐enforcing supervisor with simple structure can be obtained by reverting the SPN into a TdPN. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

On the existence of finite state supervisors for arbitrarysupervisory control problems

Given two prefix closed languages K, L ⊆ Σ*, where K ⊆ L represents the desired closed-loop behavior and L is the open-loop behavior, there exists a finite-state supervisor that enforces K in the closed loop if and only if there is a regular, prefix-closed language M ⊆ Σ*, such that: 1) MΣ_u∪L⊆M, and 2) M∪L=K. In this paper, we show that this is equivalent to: 1) the controllability of sup{P⊆K∪L¯|pr(P)=P} with respect to Σ*; and 2) the regularity of sup{P⊆K∪L¯|pr(P)=P}, where L¯=Σ*-L:and pr(·) is the set of prefixes of strings in the language argument. We use this property to investigate the issue of deciding the existence of a finite-state supervisor for different representations. We also present some properties of the language sup{P⊆K∪L¯|pr(P)=P}, along with implications to the synthesis of solutions to the supervisory control problem with the fewest states     

Reliable Decentralized Supervisory Control For Marked Language Specifications

We consider a discrete event system controlled by a decentralized supervisor consisting of n local supervisors. In our previous work, we have studied reliable decentralized supervisory control for closed language specifications. In this paper, we extend this work to the specifications given by marked languages. A decentralized supervisor is said to be k‐reliable (1 ∞ k ∞ n) if it exactly achieves a specification language without blocking under possible failures of any less than or equal to n ‐ k local supervisors. We present necessary and sufficient conditions for the existence of a k‐reliable decentralized supervisor. Then we define a weaker version of k‐reliability, called weak k‐reliability, by relaxing the nonblocking requirement. We obtain necessary and sufficient conditions for the existence of a weakly k‐reliable decentralized supervisor. Moreover, we propose an iterative scheme for computing a sublanguage of a specification for which the existence conditions of a weakly k‐reliable decentralized supervisor are satisfied.     

Bisimilarity enforcing supervisory control for deterministic specifications

This paper studies the supervisory control of nondeterministic discrete event systems to achieve a bisimulation equivalence between the controlled system and the deterministic specification. In particular, a necessary and sufficient condition is given for the existence of a bisimilarity enforcing supervisor, and a polynomial algorithm is developed to verify such a condition. When the existence condition holds, a bisimilarity enforcing supervisor is constructed. Otherwise, two methods are provided for synthesizing supremal feasible sub-specifications.     

Liveness-enforcing supervision of bounded ordinary Petri nets usingpartial 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     

Reliable decentralized supervisory control of discrete eventsystems

We consider a discrete event system controlled by a decentralized supervisor consisting of n local supervisors, and formulate a new decentralized supervisory control problem, called a reliable decentralized supervisory control problem. A decentralized supervisor is said to be k-reliable (1相似文献