Ziyue Ma

Design of Optimal Petri Net Controllers for Disjunctive Generalized Mutual Exclusion Constraints

In this paper, a type of specifications called OR-AND Generalized Mutual Exclusion Constraints (GMEC) for place/transition nets is defined. Such a specification consists of a disjunction of conjunction of several single GMECs, i.e., the requirement is that, at any given time, the controlled system should satisfy at least one set of conjunctive GMECs. We show that a bounded OR-AND GMEC can be enforced by a special control structure composed by a set of AND-GMEC monitor places plus a switcher that determines the current active ones. We also show that such a simple control structure can be modified to ensure maximal permissiveness. This approach can be used in the framework of supervisory control in Petri nets.

Characterization of Admissible Marking Sets in Petri Nets With Conflicts and Synchronizations

In this paper we study the problem of constraint transformation for Petri nets with uncontrollable transitions and containing both conflicts and synchronizations. We show that given an arbitrary net and a set of legal markings, the admissible marking set cannot always be represented by a finite number of disjunctions of GMECs. Moreover, we characterize the GMEC inflation phenomenon, that is, the case in which the representation of the admissible marking set may be too complex to be efficiently implemented in a closed-loop net. To rule out the possibility of GMEC inflation we consider a subclass of constraints called singular GMECs with an acyclic backward-conflict-free uncontrollable subnet. By these assumptions we propose an algorithm to transform a given singular GMEC into a controllable OR-GMEC which precisely characterizes its admissible marking set.

Comments on Maximally permissive supervisor synthesis based on a new constraint transformation method Automatica 48 (2012), 1097-1101

This note shows by means of simple counterexamples that some key results presented by Luo et al. on the synthesis of maximally permissive supervisors based on the Uncontrollable Transition Gain Transformation method are incorrect. As a result, the transformation of inadmissible generalized mutual exclusion constraints for Petri nets is still an open issue.

A Constraint Transformation Technique for Petri Nets with Certain Uncontrollable Structures

Abstract In this paper we study the problem of constraint transformation. We consider a special type of system in which the uncontrollable subnet is an assembly flow system, which is a subclass of backward-synchronization-backward-conflict-free Petri net. We propose an algorithm to transform a given inadmissable GMEC into an equivalent admissible OR-GMEC. The algorithm is based on a technique that adds new constraints obtained by composition of elementary ones.

Petri net controllers for disjunctive Generalized Mutual Exclusion Constraints

In this paper a type of specifications called OR-GMEC for place/transition nets is defined. Such a specification consists of a set of disjunctive Generalized Mutual Exclusion Constraint, i.e. the requirement is that, at any given time, the controlled system should satisfy at least one of them. We show that a bounded OR-GMEC can be enforced by a special control structure composed by a set of monitor places (one for each constraint) plus a switcher that determines the current active constraint. We also show that such a simple control structure is not maximally permissive, and characterize this problem identifying a special subset of transitions that may be over-restricted. A modified controller that ensures maximal permissiveness is also presented. Finally, we discuss a particular control problem, that consists in preventing the firing of a given set of transitions and show that it can be reduced to an OR-GMEC problem.

Petri net controllers for Generalized Mutual Exclusion Constraints with floor operators

In this paper a special type of nonlinear marking specifications called stair generalized mutual exclusion constraints (stair-GMECs) is defined. A stair-GMEC can be represented by an inequality whose left-hand is a linear combination of floor functions. Stair-GMECs have higher modeling power than classical GMECs and can model legal marking sets that cannot be defined by OR-AND GMECs. We propose two algorithms to enforce a stair-GMEC as a closed-loop net, in which the control structure is composed by a residue counter, remainder counters, and duplicate transitions. We also show that the proposed control structure is maximally permissive since it prevents all and only the illegal trajectories of a plant net. This approach can be applied to both bounded and unbounded nets. Several examples are proposed to illustrate the approach.

Verification of language-based opacity in Petri nets using verifier

A system is said to be language opaque if the intruder cannot infer if the generated event sequence belongs to a secret based on its partial observation. In this paper we address the problem of verifying language-based opacity in systems modeled by bounded labeled Petri nets. We generalize the notion of language opacity to strict language opacity to deal with the case where the intruder is only interested in a subset of transitions. Furthermore, we show that strict language opacity is identical to language opacity for a special class of secrets. A verifier is constructed to analyze strict language opacity under the assumption that the intruder only cares about observable transitions.

A constraint transformation technique in Petri nets with backward-conflict-free uncontrollable structures

In this paper we study the problem of constraint transformation for Petri nets. We consider a special class of systems in which the uncontrollable subnet is backward-conflict-free, and a new special class of GMECs called singular GMECs. We propose an algorithm to transform a given uncontrollable singular GMEC into an equivalent controllable OR-GMEC. The algorithm is based on the composition technique of GMECs.

Supervisory enforcement of current-state opacity with uncomparable observations

Current-state opacity is a key security property in discrete event systems. A system is said to be current-state opaque if the intruder, who only has partial observations on the systems evolution, is never able to infer that the current state of the system is within a set of secret states. In this work, we address the problem of enforcing current-state opacity by supervisory control. Given a system that is modeled with a finite automaton and that is not current-state opaque with respect to a given secret, the enforcement problem consists in designing a supervisor so that the controlled system is current-state opaque. We assume that the supervisor can only observe and control a subset of events. To be more general, we assume no specific containment relationship exists between the sets of events that can be observed by the intruder and the supervisor, respectively. We call this general setting uncomparable observations. We show that the maximally permissive supervisor always exists and propose a novel approach for its design.

An Approach To Determine Controllability of Monolithic Supervisors

Abstract In this paper we study the problem of supervisory design using Petri nets. We consider a monolithic supervisor candidate, i.e., a net obtained by concurrent composition of plant and specification, and we say that the control problem has an OR-AND GMEC solution if the set of the legal markings of such a net can be described by a disjunction/conjunctions of linear constraints. We derive some sufficient conditions, based on the boundedness of some places of the net, for the existence of such a solution.