Control Of Discrete Event Systems Research Articles

Bisimilarity enforcing supervisory control of nondeterministic discrete event systems with nondeterministic specifications

We consider a bisimilarity control problem for the plant and the specification modeled as nondeterministic automata. This problem requires us to synthesize a nondeterministic supervisor such that the supervised plant is bisimilar to the specification. We derive a new necessary and sufficient condition for the existence of a supervisor that solves the bisimilarity control problem. Although the complexity of verifying this existence condition is exponential in the numbers of states of the plant and the specification, it is smaller than that of the exhaustive search that uses the existing condition. We present how to synthesize a solution to the bisimilarity control problem if it exists. In addition, we give a polynomially verifiable necessary condition.

Structural Controller for Logical Expression of Linear Constraints on Petri Nets

Based on the P-type composition of Petri nets (PNs) defined in this paper, a framework for a structural control of discrete event systems (DESs) is constructed such that a closed-loop PN is obtained by composing a plant PN and a controller. As for a disjunction or conjunctive normal form (CNF) of linear constraints, a new approach is proposed to design a structural controller in this framework. First, a switching-net is defined for a disjunction of constraints, and an extended plant is obtained through the P-type composition of a plant PN and switching-net. Second, the disjunction of bounded constraints is transformed into a conjunction of switching-constraints on the extended plant. Third, a controller is synthesized by designing monitors for conjunctive switching-constraints according to a supervision-based-on-place-invariant method. Fourth, in a similar manner, a controller is also designed for a CNF of bounded constraints. The resulting controller is maximally permissive if each disjunction of constraints meets the jump-free condition, and its size grows polynomially with the number of constraints. Another advantage is that the closed-loop system is still a PN for many real DES since a CNF can describe not only convex but also nonconvex state regions.

Suboptimal time management of discrete event systems with uncontrollable events modeled by Petri nets

AbstractPreventing systems from entering to forbidden states is a crucial issue in discrete event systems control. Adding supervisors to the system is a common method to avoid entering to forbidden states. In discrete event systems modeled by Petri net adding a supervisor could be done by means of control places. Since, the time is not considered in designing this supervisor, in presence of uncontrollable transitions adding control places can lead to increase the operation time of the system modeled by timed Petri net. Because, the firing of some transitions is prevented when it is not necessary. So, to design a more efficient controller, we will be required to use time information of the system component. Therefore, in this paper, a method for optimizing the time behavior of a supervised timed Petri net will be proposed. To obtain an efficient operation, some timed places as timer will be added to the net. The time of this timer places is calculated to permit firing of some controllable transitions in order to enter into some weakly forbidden states while entering to forbidden states is prevented. This concept leads to increase the speed of system as well as obtain an acceptable operation. This method can be applied for all systems modeled by Petri nets. The efficiency of proposed approach will be discussed and validated with a case study.

Reconfiguration Control of Dynamic Reconfigurable Discrete Event Systems Based on NCESs

In order to satisfy system specifications persistently in the cases of component failure, partial communication blocks, or energy deficiency, safety-critical systems need to apply system reconfigurations at runtime. Such systems can be considered as dynamic reconfigurable discrete event systems (DRDESs) if their logic behaviors are concerned only. A reconfiguration of a DRDES includes the switch of system structures and the update of system states. Based on the assumption that all configurations of a DRDES are designed in advance and dynamic reconfigurations can be implemented only at a few predefined reconfigurable states, a novel reconfiguration control method is proposed in this paper. The aim is to implement a required dynamic reconfiguration smoothly and rapidly. A DRDES is modeled by net condition/event systems (NCESs) under the firing rule “maximal single spontaneous transition steps.” An integer linear programming-based method is developed to compute a shortest legal firing sequence (SLFS) from the state where a reconfiguration requirement arises to a reconfigurable state. Accordingly, a virtual controller for guiding the system to evolve along the obtained SLFS is proposed. The proposed method is able to implement a required reconfiguration before the maximum permissible reconfiguration delay if an SLFS exists. A simple reconfigurable assembly system is adopted to illustrate the method.

Approximated timed reachability graphs for the robust control of discrete event systems

This paper is about control sequences design for Discrete Event Systems (DES) modeled with Time Petri nets (TPN) including a set of temporal specifications. Petri nets are known as efficient mathematical and graphical models that are widely used to describe distributed DES including choices, synchronizations and parallelisms. The domains of application include but are not restricted to manufacturing systems, computer science and transportation networks. Incorporating the time in the model is important to consider many control problems such as scheduling and planning. This paper solves some control issues in timed context and uncertain environments that include unexpected events modeled with uncontrollable transitions. To deal with such uncertainties, we propose first to build an Approximated Timed Reachability Graph that includes the time specifications and model all feasible timed trajectories at a given accuracy under earliest firing policy. Then, this graph is used to search optimal paths by using an approach based on Markov Decision Processes that encode the environment uncertainties. Such optimal paths lead to near-optimal solutions for the TPN. Several simulations illustrate the benefit of the proposed method from the performance and computational points of view.

Maximally Permissive Nonblocking Supervisors for Similarity Control of Nondeterministic Discrete Event Systems under Event and State Observations

Maximally Permissive Nonblocking Supervisors for Similarity Control of Nondeterministic Discrete Event Systems under Event and State Observations

Petri Nets at Modelling and Control of Discrete-Event Systems with Nondeterminism -- Part 2

Discrete-Event Systems (DES) are discrete in nature. Petri Nets (PN) are one of the most widespread tools for DES modelling, analyzing and control. Different kinds of PN can be used for such purposes. Some of them were described in [3], being the first part of this paper. Here, the applicability of Labelled PN (LbPN) and Interpreted PN (IPN) for modelling and control of nondeterministic DES, especially with uncontrollable and/or unobservable transitions in the models, will be pointed out. Moreover, another kinds of nondeterminism in DES (errors, failures) will be modelled, and the possibilities of the error recovery of failed system will be presented.

Discrete-Event Systems Supervisory Control for a Custom Power Park

This paper investigates the application of supervisory control of discrete event system (SCDES) to the management and control of a custom power park (CPP). The heterogeneous nature of upcoming devices and equipment in CPP require advanced control methods to ensure the integrity and reliability under different operational states. A solution to achieve appropriate controllability, while avoiding complexity, is to sub-divide the control problem based on event-triggered dynamics where the occurrence of specific events could change the state of the system. This idea is employed to formulate the problem of coordination of the devices in a CPP and develop a systematic method to design a supervisory control based on the theory of SCDES. Three modular supervisors are synthesized using the TCT software and simulated using the Simulink. The proposed methodology could be applied to several control problems in microgrids.

Decentralized Supervisory Control of Discrete Event Systems: An Arborescent Architecture to Realize Inference-Based Control

The two simplest language-based decentralized controls of discrete event systems are called conjunctive and permissive (C&P) and disjunctive and antipermissive (D&A) controls. On the other side, inference-based control is the most general language-based decentralized control. In this paper, we propose a decentralized control method, called arborescent control, which constructs and uses a tree-like control architecture that depends on the control objective. Each node $n$ of the tree is a disjunction or conjunction of the enabling/disabling decisions of the two children of $n$ . We show that if inference-based control is applicable to the control objective, then every leaf of the obtained tree is a C&P or D&A control. This means that by combining adequately C&P and D&A controls, we can realize every control objective that is realizable by inference-based control.

How selfish individuals achieve unselfish goals: majority-based progressive control of discrete event systems

ABSTRACT We present majority-based progressive control in which local supervisors have not only their own private specifications as primary goals, but an additional global specification representing a desirable behavior of the overall system. The control policy follows the majority rule, and the ultimate goal is to achieve a progressive closed-loop behavior whereby the number of local supervisors meeting private specifications increases as the controlled system evolves. For this purpose, we present the notion of majority-controllability of a global specification, and show that it is a crucial condition for the existence of local supervisors achieving a progressive global specification. Using the presented control theory, we analyze how the federal estate tax in the Unites States was repealed in 2010.

Synthesis of minimally restrictive optimal stability-enforcing supervisors for nondeterministic discrete event systems

In this paper, we investigate stability-enforcing supervisory control of nondeterministic discrete event systems (DESs) from a brand-new angle. First, the dynamics of a discrete event system (DES) are converted into an algebraic equation in the framework of Boolean semi-tensor product. Using it, several necessary and sufficient conditions are presented to verify whether a DES is stable or not. Second, effective verification criteria are provided for the stabilization problem of DESs. Further, a cost function of disabling controllable events at corresponding states is defined. A matrix-based methodology of finding all minimally restrictive optimal stability-enforcing supervisors is presented. Finally, two examples are provided to illustrate the theoretical results.

Application of online supervisory control of discrete-event systems to multi-robot warehouse automation

In this paper we present an online supervisory control approach, based on limited lookahead policy, that is amenable for the control of multi-agent discrete-event systems. We then apply this online control scheme to model and control a warehouse automation system served by multiple mobile robots; the effectiveness of this scheme is demonstrated through a case study. Moreover, we build an experiment testbed for testing the validity of our proposed method with implementation on real robots.

Supervisory Control of Discrete-Event Systems Under Attacks

We consider a multi-adversary version of the supervisory control problem for discrete-event systems (DES), in which an adversary corrupts the observations available to the supervisor. The supervisor’s goal is to enforce a specific language in spite of the opponent’s actions and without knowing which adversary it is playing against. This problem is motivated by applications to computer security in which a cyber defense system must make decisions based on reports from sensors that may have been tampered with by an attacker. We start by showing that the problem has a solution if and only if the desired language is controllable (in the DES classical sense) and observable in a (novel) sense that takes the adversaries into account. For the particular case of attacks that insert symbols into or remove symbols from the sequence of sensor outputs, we show that testing the existence of a supervisor and building the supervisor can be done using tools developed for the classical DES supervisory control problem, by considering a family of automata with modified output maps, but without expanding the size of the state space and without incurring on exponential complexity on the number of attacks considered.

SPECIAL ISSUE: Modelling, Simulation, and Control of Discrete Event Systems

SPECIAL ISSUE: Modelling, Simulation, and Control of Discrete Event Systems

Supervisory control of state-tree structures with partial observation

Supervisory control of discrete-event systems (SCDES) is well developed to find a maximally permissive supervisor. As an extension to supervisory control theory, a new framework, state-tree structures (STS), has been deployed to manage the state explosion problem of SCDES. This paper aims to address this notorious issue of supervisory control with partial observation in the STS framework by state feedback control that calculates the controllers of the controllable-observable events only, which is realized by the following two steps. First, for a specification represented as a predicate, a supremal normal subpredicate that requires only the controllable-observable events enabled/disabled, is computed. Second, according to the new transition function constructed by the natural projection of the given STS, the supremal nonblocking, weakly controllable subpredicate is obtained from the supremal normal subpredicate. The proposed approach based on STS provides the possibility to supervise controllable events under partial observation in large-scale systems with the state explosion problem managed. An example with state size over 107 that leads to program crashes in SCDES can be solved in this paper. Moreover, in order to demonstrate the industrial applications of the contribution of this research, three examples are addressed.

Exploiting Distinguishers in Local Modular Control of Discrete-Event Systems

Local modular control (LMC) is an approach to the supervisory control theory (SCT) of discrete-event systems that exploits the modularity of plant and specifications. Recently, distinguishers and approximations have been associated with SCT to simplify modeling and reduce synthesis effort. This paper shows how advantages from LMC, distinguishers, and approximations can be combined. Sufficient conditions are presented to guarantee that local supervisors computed by our approach lead to the same global closed-loop behavior as the solution obtained with the original LMC, in which the modeling is entirely handled without distinguishers. A further contribution presents a modular way to design distinguishers and a straightforward way to construct approximations to be used in local synthesis. An example of manufacturing system illustrates our approach. Note to Practitioners — Distinguishers and approximations are alternatives to simplify modeling and reduce synthesis cost in SCT, grounded on the idea of event-refinements. However, this approach may entangle the modular structure of a plant, so that LMC does not keep the same efficiency. This paper shows how distinguishers and approximations can be locally combined such that synthesis cost is reduced and LMC advantages are preserved.

Supervisor localisation for large-scale discrete-event systems under partial observation

ABSTRACTRecently we developed partial-observation supervisor localisation, a top-down approach to distributed control of discrete-event systems (DES) under partial observation. Its essence is the decomposition of the partial-observation monolithic supervisor into partial-observation local controllers for individual controllable events. In this paper, we extend the partial-observation supervisor localisation to large-scale DES, for which the monolithic supervisor may be incomputable. Specifically, we first employ an efficient heterarchical supervisor synthesis procedure to compute a heterarchical array of partial-observation decentralised supervisors and partial-observation coordinators. Then, we localise each of these supervisors/coordinators into partial-observation local controllers. This procedure suggests a systematic approach to the distributed control of large-scale DES under partial observation. The results are illustrated by a system of automatic guided vehicles serving a manufacturing workcell.

Algorithms of reduced complexity to design control sequences for untimed Petri nets in varying and uncertain environments

Petri nets have been widely used for the modelling, analysis, control and optimization of discrete event systems with shared resources in the domains of engineering. This article concerns the design of control sequences for such systems modelled with untimed Petri nets. The aim of the controller is to incrementally compute sequences of transition firings with minimal size. Such sequences aim to move the marking from an initial value to a reference value. The resulting trajectory must avoid some forbidden markings and limit as possible the exploration of non-promising branches. For this purpose, the approach explores a small part of the reachability graph in the neighbourhood of the current marking. Then from the explored markings, it estimates a distance to the reference. The main contributions are (a) to reduce the explored part of the reachability graph according to a double limitation in breadth and in depth in order to provide solutions with a low computational effort; (b) to provide conditions to ensure the converge and optimality of the proposed algorithms and derive necessary and sufficient conditions for reachability; and (c) to include the firing sequence design in a global control schema suitable for reactive scheduling problems in uncertain and perturbed environments. The main application concerns deadlock-free scheduling problems in the domain of flexible manufacturing systems, but the approach is also applicable for systems in computer science and transportation.

Guest editorial: special issue on diagnosis, opacity and supervisory control of discrete event systems

Guest editorial: special issue on diagnosis, opacity and supervisory control of discrete event systems

State‐Feedback Control for a Class of Timed Petri Nets Subject to Marking Constraints

AbstractThe paper contributes with an original method of designing a control for discrete event systems modeled by a class of timed Petri nets. Precisely, this work deals with the closed loop control of Timed Event Graphs (TEGs) under specifications expressed with linear marking constraints. The objective of the controller is to limit the number of tokens in some places of these TEGs. The behavior of TEGs is represented by a system of difference equations that are linear in Min‐Plus algebra and the constraints are described by a set of inequalities, which are also linear in Min‐Plus algebra. A formal approach to design control laws that guarantee compliance with these marking constraints is proposed. For this, two sufficient conditions for the existence of control laws are proposed. The computed controls are causal feedbacks, which can be represented by a set of marked and timed places. The proposed method is illustrated in two applications: a manufacturing production line and an assembly system.