On the Enforcement of a Class of Nonlinear Constraints on Petri Nets

International audienceThis paper focuses on the enforcement of nonlinear constraints in Petri nets. First, a supervisory structure is proposed for a nonlinear constraint. The proposed structure consists of added places and transitions. It controls the transitions in the net to be controlled only but does not change its states since there is no arc between the added transitions and the places in the original net. Second, an integer linear programming model is proposed to transform a nonlinear constraint to a minimal number of conjunc-tive linear constraints that have the same control performance as the nonlinear one. By using a place invariant based method, the obtained linear constraints can be easily enforced by a set of control places. The control places consist to a supervisor that can enforce the given nonlinear constraint. On condition that the admissible markings space of a nonlinear constraint is non-convex, another integer linear programming model is developed to obtain a minimal number of constraints whose disjunctions are equivalent to the nonlinear constraint. Finally, a number of examples are provided to demonstrate the proposed approach

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

Practical Distributed Control Synthesis

Classic distributed control problems have an interesting dichotomy: they are either trivial or undecidable. If we allow the controllers to fully synchronize, then synthesis is trivial. In this case, controllers can effectively act as a single controller with complete information, resulting in a trivial control problem. But when we eliminate communication and restrict the supervisors to locally available information, the problem becomes undecidable. In this paper we argue in favor of a middle way. Communication is, in most applications, expensive, and should hence be minimized. We therefore study a solution that tries to communicate only scarcely and, while allowing communication in order to make joint decision, favors local decisions over joint decisions that require communication.Comment: In Proceedings INFINITY 2011, arXiv:1111.267

Supervisor Synthesis for Discrete Event Systems under Partial Observation and Arbitrary Forbidden State Specifications

In this paper, we consider the forbidden state problem in discrete event systems modeled by partially observed and partially controlled Petri nets. Assuming that the reverse net of the uncontrollable subnet of the Petri net is structurally bounded, we compute a set of weakly forbidden markings from which forbidden markings can be reached by firing a sequence of uncontrollable/unobservable transitions. We then use reduced consistent markings to represent the set of consistent markings for Petri nets with structurally bounded unobservable subnets. We determine the control policy by checking if the firing of a certain controllable transition will lead to a subsequent reduced consistent marking that belongs to the set of weakly forbidden markings; if so, we disable the corresponding controllable transition. This approach is shown to be minimally restrictive in the sense that it only disables behavior that can potentially lead to a forbidden marking. The setting in this paper generalizes previous work by studying supervisory control for partially observed and partially controlled Petri nets with a general labeling function and a finite number of arbitrary forbidden states. In contrast, most previous work focuses on either labeling functions that assign a unique label to each observable transition or forbidden states that are represented using linear inequalities. More importantly, we demonstrate that, in general, the separation between observation and control (as considered in previous work) may not hold in our setting

A branch and bound approach for the design of decentralized supervisors in Petri net models

The paper addresses the design of compact and maximally permissive decentralized supervisors for Petri nets, based on generalized mutual exclusion constraints. Decentralization constraints are formulated with respect to the net transitions, instructing each local supervisor to detect and disable transitions of its own control site only. A solution is characterized in terms of the states it allows and its feasibility is assessed by means of two separate tests, one checking the required behavioral properties (e.g., liveness, reversibility and controllability) of the induced reachability subgraph and the other ensuring the existence of a decentralized supervisor enforcing exactly the considered set of allowed states. The second test employs an integer linear programming formulation. Maximal permissivity is ensured by efficiently exploring the solution space using a branch and bound method that operates on the reachable states. Particular emphasis is posed on the obtainment of the controllability property, both in the structural and the behavioral interpretation

Continuous flow Systems and Control Methodology Using Hybrid Petri nets

International audienceIn this paper, we consider the controller synthesis for continuous flow systems. These lasts are a sub-class of hybrid dynamic systems. Their main characteristics are positiveness and linearity. Transport, manufacturing, communication and biological systems are examples of continuous flow systems. Numerous tools and techniques exist in the literature for modelling and analyzing such systems. As positiveness is a hard constraint, an appropriate tool integrating naturally this constraint is strongly needed. Hybrid Petri Nets are an elegant modeling tool of positive systems, while Hybrid Automata are a powerful tool giving formally the reachable dynamic space. Combining these two tools aim to a sound approach for control synthesis of continuous flow systems. We start by considering the process to control and compute its reachable state space using specialized software like PHAVer. Algebraic inequalities define this reachable state space. The constrained behaviour is obtained by restricting this state space into a smaller desired space. This reduction is expressed in term of linear constraints only over the continuous variables; while the control is given by the discrete transitions (occurrence dates of controllable events). The controller synthesis methodology is based on the control of a hybrid system modelled by a D-elementary hybrid Petri Net. The control consists in modifying the guard of the controllable transitions so as the reachable controlled state space is maximally permissive

Supervisory Control and Analysis of Partially-observed Discrete Event Systems

Nowadays, a variety of real-world systems fall into discrete event systems (DES). In practical scenarios, due to facts like limited sensor technique, sensor failure, unstable network and even the intrusion of malicious agents, it might occur that some events are unobservable, multiple events are indistinguishable in observations, and observations of some events are nondeterministic. By considering various practical scenarios, increasing attention in the DES community has been paid to partially-observed DES, which in this thesis refer broadly to those DES with partial and/or unreliable observations. In this thesis, we focus on two topics of partially-observed DES, namely, supervisory control and analysis. The first topic includes two research directions in terms of system models. One is the supervisory control of DES with both unobservable and uncontrollable events, focusing on the forbidden state problem; the other is the supervisory control of DES vulnerable to sensor-reading disguising attacks (SD-attacks), which is also interpreted as DES with nondeterministic observations, addressing both the forbidden state problem and the liveness-enforcing problem. Petri nets (PN) are used as a reference formalism in this topic. First, we study the forbidden state problem in the framework of PN with both unobservable and uncontrollable transitions, assuming that unobservable transitions are uncontrollable. For ordinary PN subject to an admissible Generalized Mutual Exclusion Constraint (GMEC), an optimal on-line control policy with polynomial complexity is proposed provided that a particular subnet, called observation subnet, satisfies certain conditions in structure. It is then discussed how to obtain an optimal on-line control policy for PN subject to an arbitrary GMEC. Next, we still consider the forbidden state problem but in PN vulnerable to SD-attacks. Assuming the control specification in terms of a GMEC, we propose three methods to derive on-line control policies. The first two lead to an optimal policy but are computationally inefficient for large-size systems, while the third method computes a policy with timely response even for large-size systems but at the expense of optimality. Finally, we investigate the liveness-enforcing problem still assuming that the system is vulnerable to SD-attacks. In this problem, the plant is modelled as a bounded PN, which allows us to off-line compute a supervisor starting from constructing the reachability graph of the PN. Then, based on repeatedly computing a more restrictive liveness-enforcing supervisor under no attack and constructing a basic supervisor, an off-line method that synthesizes a liveness-enforcing supervisor tolerant to an SD-attack is proposed. In the second topic, we care about the verification of properties related to system security. Two properties are considered, i.e., fault-predictability and event-based opacity. The former is a property in the literature, characterizing the situation that the occurrence of any fault in a system is predictable, while the latter is a newly proposed property in the thesis, which describes the fact that secret events of a system cannot be revealed to an external observer within their critical horizons. In the case of fault-predictability, DES are modeled by labeled PN. A necessary and sufficient condition for fault-predictability is derived by characterizing the structure of the Predictor Graph. Furthermore, two rules are proposed to reduce the size of a PN, which allow us to analyze the fault-predictability of the original net by verifying that of the reduced net. When studying event-based opacity, we use deterministic finite-state automata as the reference formalism. Considering different scenarios, we propose four notions, namely, K-observation event-opacity, infinite-observation event-opacity, event-opacity and combinational event-opacity. Moreover, verifiers are proposed to analyze these properties

Service substitution : a behavioral approach based on Petri Nets

Service-Oriented Computing is an emerging computing paradigm that supports the modular design of (software) systems. Complex systems are designed by composing less complex systems, called services. Such a (complex) system is a distributed application often involving several cooperating enterprises. As a system usually changes over time, individual services will be substituted by other services. Substituting one service by another one should not affect the correctness of the overall system. Assuring correctness becomes particularly challenging, as the services rely on each other, and each of the involved enterprises only oversees a part of the overall system. In addition, services communicate asynchronously which makes the analysis even more difficult. For this reason, formal methods to support service substitution are indispensable. In this thesis, we study service substitution at the level of service models. Thereby we restrict ourselves to service behavior. As a formalism to model service behavior, we use Petri nets. The first contribution of this thesis is the definition of several substitutability criteria that are suitable in the context of Service-Oriented Computing. Substituting a service S by a service S0 should preserve some behavioral properties of the overall system. For each set of behavioral properties and a given service S, there exists a set of behaviorally compatible services for S. A substitutability criterion defines which of these behaviorally compatible services of S have to be preserved by S0. We relate our substitutability criteria to preorders and equivalences known from process theory. The second contribution of this thesis is to present, for each substitutability criterion, a procedure to decide whether a service S0 can substitute a service S. The decision requires the comparison of the in general infinite sets of behaviorally compatible services for the services S and S0. Hence, we extend existing work on an abstract representation of all behaviorally compatible services for a given service. For each notion of behavioral compatibility, we present an algorithmic solution to represent all behaviorally compatible services. Based on these representations, we can decide substitutability of a service S by a service S0. The third contribution of this thesis is a method to support the design of a service S0 that can substitute a service S according to a substitutability criterion. Our approach is to derive a service S0 from the service S by stepwise transformation. To this end, we present several transformation rules. Finally, we formalize and we extend the equivalence notion for services specified in the language WS-BPEL. That way, we demonstrate the applicability of our work

Observer design for weighted timed event graphs in a dioid framework

An observer is used in a feedback control system to compensate for the fact that not all states can be measured. This work refers to systems that can be modeled by timed Petri nets, more precisely, Weighted Timed Event Graphs (WTEGs). The WTEG allows modeling of problems without conflicts of resources. In the context of manufacturing systems, WTEGs are appropriate to design complex assembly lines, where dynamic behavior is described by the synchronization and saturation effects. We propose the design of an observer for WTEGs that, which consists of: (i) an Optimal Observer that is based on the conversion of the WTEG to the Timed Event Graph(TEG), which has a linear representation in the mathematical structure of the dioids; (ii) a Simulator, which is a copy of the system without disturbances; (iii) and an Interface that is used to connect the WTEG to the Optimal Observer and to the Simulator.Um observador é utilizado em um sistema de controle por realimentação, para compensar o fato de que nem todos os estados podem ser medidos. Esse trabalho aborda sistemas que podem ser modelados por redes de Petri temporizadas, mais precisamente, por Grafos de Eventos Temporizados Ponderados (WTEGs). A estrutura do WTEG permite a modelagem de problemas sem conflitos de recursos. No contexto de sistemas de manufatura, os WTEGs são apropriados para reproduzir linhas de montagem complexas, em que o comportamento dinâmico é descrito pelos efeitos de sincronização e saturação. Neste trabalho é proposto o projeto de um observador para WTEGs que consiste na construção: (i) do Observador Otimo que se baseia na conversão do WTEG para o Grafo de Evento Temporizado (TEG), o qual possui uma representação linear na estrutura matemática dos dióides; (ii) do Simulador, que é uma cópia do sistema sem os distúrbios; (iii) e da Interface que é utilizada para conectar o WTEG ao Observador Otimo e ao Simulador