Supervisor synthesis for bounded Petri nets based on a transformation function

FEEDBACK CONTROL LOGIC FOR BACKWARD CONFLICT FREE CHOICE NETS

To enforce linear constraints on Petri nets that are partially controllable and observable, this work proposes an approach based on constraint transformation. First, a state-space equation of a Petri net control system based on event feedback is obtained by expressing a control action as a matrix, and the optimal control policy is designed. However, this policy needs to solve a nonlinear program on line. Second, pre-transition-gain-transformation is proposed to equivalently transform a constraint into a disjunction of new ones for an uncontrollable transition, and, similarly, post-transition-gain-transformation to transform a constraint into a disjunction of new ones for an unobservable transition. An algorithm is then given to transform a constraint into a disjunction of admissible ones, and, consequently, an efficient policy, which may not be optimal, can be designed. Third, in order to guarantee that the policy be both efficient and optimal, a dynamic linear constraint is introduced. Further, observing-transformation is proposed to simplify a dynamic constraint for an unobservable transition, and an algorithm is given to equivalently transform a class of linear constraints into admissible dynamic ones. As a result, an optimal controller requiring little online computation can be designed accordingly for some class of Petri nets. Finally, a maze system is used to illustrate the theoretical results.

The recently introduced method, which was called ldquostretching,rdquo is extended to timed Petri nets which may have both controllable and uncontrollable transitions. Using this method, a new Petri net, called ldquostretched Petri net,rdquo which has only unit firing durations, is obtained to represent a timed-transition Petri net. Using this net, the state of the original timed Petri net can be represented easily. This representation also makes it easy to design a supervisory controller for a timed Petri net for any purpose. In this paper, supervisory controller design to avoid deadlock is considered in particular. Using this method, a controller is first designed for the stretched Petri net. Then, using this controller, a controller for the original timed Petri net is obtained. Algorithms to construct the reachability sets of the stretched and original timed Petri nets, as well as algorithms to obtain the controller for the original timed Petri net are presented. These algorithms are implemented using Matlab. Examples are also presented to illustrate the introduced approach.

In this paper, the synthesis of bounded Petri nets from deterministic modal transition systems is shown to be undecidable. The proof is built from three components. First, it is shown that the problem of synthesising bounded Petri nets satisfying a given formula of the conjunctive nu-calculus (a suitable fragment of the mu-calculus) is undecidable. Then, an equivalence between deterministic modal transition systems and a language-based formalism called modal specifications is developed. Finally, the claim follows from a known equivalence between the conjunctive nu-calculus and modal specifications.

This paper deals with the problem of forbidden states in Discrete Event Systems modelled by non‐safe Petri Nets. To avoid these states, some Generalized Mutual Exclusion Constraints can be assigned to them. These constraints limit the weight sum of tokens in some places and can be enforced on the system using control places. When the number of these constraints is large, a large number of control places should be added to the system. In this paper, a method is presented to assign the small number of constraints to forbidden states using some states which cover the forbidden states. So, a small number of control places are added to the system leading to obtaining a maximally permissive controller.

Results in the literature have provided efficient control synthesis techniques for the problem of deadlock avoidance in Petri nets. These results are shown to fit within an established framework for the enforcement of linear constraints on the marking behavior of a net. Framing the problem in this way allows uncontrollable and of unobservable transitions to be included in the plant model when deadlock avoidance is performed.

This paper addresses the problem of current-state opacity of discrete event systems (DES) modeled with Petri nets. A system is said to be current-state opaque if the intruder who only has partial observations on the system's behavior is never able to infer that the current state of the system is within a set of secret states. Based on the notion of basis markings, an efficient approach to verifying current-state opacity in bounded Petri nets is proposed, without computing the whole reachability set or exhaustively enumerating the set of markings consistent with the observation. An example showing the efficiency of the approach is presented.

This paper presents an algorithm for the synthesis of bounded Petri nets from transition systems. A bounded Petri net is always provided in case it exists. Otherwise, the events are split into several transitions to guarantee the synthesis of a Petri net with bisimilar behavior. The algorithm uses symbolic representations of multisets of states to efficiently generate all the minimal regions. The algorithm has been implemented in a tool. Experimental results show a significant net reduction when compared with approaches for the synthesis of safe Petri nets.

This paper presents a generalization of forbidden state control synthesis methods for a broad class of controlled Petri nets (CtlPN). An algebra is defined for characterizing the interaction of paths in the Petri net. Given a specification of a forbidden marking set, the net structure is analyzed to determine an algebraic expression to represent the specification. For any net marking (state), evaluation of the expression will indicate whether forbidden markings are reachable and whether control is necessary. The expression is then used for efficiently determining the maximally permissive controls for the marking. >

Security of distributed control systems is affected by the presence of information leaks, which permit to external intruders to infer the state of the system itself. Noninterference deals with the absence of such leak paths in a dynamic system modeled as discrete-event system. For a system that presents information leaks, a supervisory control strategy to enforce noninterference is proposed in this article. The approach is based on the solution of optimization problems on a Petri net model of the system under investigation. The effectiveness of the proposed enforcement strategy is shown by means of illustrative examples.

State-Partition-Based Control of Discrete Event Systems for Enforcement of Regular Language Specifications

For practical automated manufacturing systems (AMSs), the time dimension is of great significance and should be integrated in their plant models. Reasonably, many of the realistic general mutual exclusion constraints (GMECs) imposed on these discrete models should be timed rather than merely algebraic or logic. In the past, such a problem was studied on the basis of the Ramadge-Wonham supervisory control technique (SCT) and the theory of regions. It proves to be NP-hard since it necessitates the generation of reachability graphs. This paper shows that it can be solvable in polynomial time by using generalized linear constraints, which are originally proposed to increase the expressive power of the linear marking constraints. By dividing each constraint into marking, firing vector, and Parikh terms, its respective control place can be synthesized algebraically without considering the separation of dangerous states and events. Several examples are used to validate the effectiveness and efficiency of the proposed approach.

This paper deals with the control problem of forbidden states in discrete event systems. The plant model is described by a coloured Petri net and its evolving by an optimized state graph, called symbolic reachability graph. The problem is studied in the general framework of Ramadge and Wonham theory considering uncontrollable transitions and under nonblockingness requirement. The synthesis method computes a maximally permissive coloured Petri net controller. First, the symbolic reachability graph is considered to determine the legal behaviour that the plant model should have. Then, the theory of regions is applied in order to generate a maximally permissive controller. This controller is expressed in coloured Petri net terms and, is connected to the plant model. The proposed approach exploits the benefits of the parameterized modeling power of coloured Petri nets as well as the reduced size of the symbolic reachability graph.

Usually, the maximally permissive control of Petri nets with an OR-logic constraint is difficult to implement. In this paper, OR-logic is easily enforced using a colored Petri net. A colored Petri net place, named colored monitor place, is designed to monitor the states of constraints. A so-called guard function of colored Petri nets that maps certain transitions into a Boolean expression is suitably defined on the colored sets. The maximally permissive control is then obtained via the guard function. In addition, a constraint transformation method for marked graphs with uncontrollable transitions is proposed.

Currently used methods for the analysis of contingency tables with log-linear models and their extensions are essentially a way to subject the parameters of the saturated model to a set of linear constraints. However, in many contexts, expecially when a subset of the variables are ordinal, it would be very useful to be able to consider also linear inequality constraints. In this paper we show how to extend previous models for contingency tables by considering simultaneously both equality constraints. We also give a self contained discussion of the problem of testing equality and inequality constraints in the context of contingency tables analysis.