Control of a class of discrete event systems with disturbances and capacity constraints: Application to a disassembly problem

This study proposes an analytical control method for the meeting of capacity constraints in discrete event systems with disturbances. More precisely, it consists of computing control laws for partially controllable and observable timed event graphs that are subject to marking constraints. To resolve the issue, linear Min-Plus models are used to describe the behavior of these graphs, and the constraints are expressed by inequalities in Min-Plus algebra. Sufficient conditions for the existence of causal control laws to guarantee marking specifications are established. Finally, to illustrate the efficiency of the proposed approaches in this paper, an application for a disassembly process with some disturbance inputs and limited component capacities is carried out.     

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

Preventing 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.     

Feedback control for a class of discrete event systems with critical time

This paper presents an algebraic approach for control laws synthesis of timed event graphs subjected to strict temporal constraints. This class of discrete event systems is deterministic, in the sense that its behaviour only depends on the initial marking and on the control that is applied. This behaviour can be modelled by a linear equations system in Min-Plus algebra. The temporal constraint is represented by an inequality that is also linear in the Min-Plus algebra. Then, a method for the synthesis of control laws ensuring the respect of constraints is described. We give explicit formulas characterising a control law, which ensures the validity of the temporal constraints. It is a causal feedback control, involving delays. The method is illustrated on an example.     

A control synthesis approach for time discrete event systems

In this paper, we introduce a control synthesis method for discrete event systems whose behavior is dependent on explicit values of time. Our goal is to control the occurrence dates of the controllable events so that the functioning of the system respects given specifications. The system to be controlled is modeled by a time Petri net. In a previous work we proposed a systematic method to build the timed automaton which models the exact behavior of a time Petri net. Furthermore, the forbidden behaviors of the system are modeled by forbidden timed automaton locations. This paper focuses on the control synthesis method, which consists in computing new firing conditions for the timed automaton transitions so that the forbidden locations are no longer reachable.     

Feedback stabilization of some event graph models

The authors introduce several notions of stability for event graph models, timed or not. The stability is similar to the boundedness notion for Petri nets. The event graph models can be controlled by an output feedback which takes information from some observable transitions and can disable some controllable transitions. The controller itself is composed of an event graph. In this framework the authors solve the corresponding stabilization problems, i.e., they wonder if such a controller may prevent the explosion of the number of tokens     

Gradient-based controllers for timed continuous Petri nets

This paper is about control design for timed continuous Petri nets that are described as piecewise affine systems. In this context, the marking vector is considered as the state space vector, weighted marking of place subsets are defined as the model outputs and the model inputs correspond to multiplicative control actions that slow down the firing rate of some controllable transitions. Structural and functional sensitivity of the outputs with respect to the inputs are discussed in terms of Petri nets. Then, gradient-based controllers (GBC) are developed in order to adapt the control actions of the controllable transitions according to desired trajectories of the outputs.     

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

The 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.     

Robust supervisory control of a class of timed discrete event systems under partial observation

This paper studies robust supervisory control of timed discrete event systems proposed by Brandin and Wonham. Given a set of possible models which includes the exact model of the plant, the objective is to synthesize a robust supervisor such that it achieves legal behavior for all possible models. We show that controllability for each possible model and observability for a suitably defined aggregate model are necessary and sufficient conditions for the existence of a solution to the robust supervisory control problem. Moreover, when there does not exist a solution, a maximally permissive robust supervisor is synthesized under the assumption that all controllable events are observable.     

Control of discrete event systems with respect to strict duration: Supervision of an industrial manufacturing plant

In this paper, we propose a (max, +)-based method for the supervision of discrete event systems subject to tight time constraints. Systems under consideration are those modeled as timed event graphs and represented with linear (max, +) state equations. The supervision is addressed by looking for solutions of constrained state equations associated with timed event graph models. These constrained state equations are derived by reducing duration constraints to elementary constraints whose contributions are injected in the system’s state equations. An example for supervisor synthesis is given for an industrial manufacturing plant subject to a strict temporal constraint, the thermal treatment of rubber parts for the automotive industries. Supervisors are calculated and classified according to their performance, considering their impact on the production throughput.     

随机计时离散事件系统的软控制任务研究

本文通过引入马氏决策过程中的迭代算法,研究了计时离散事件系统的随机优化监控综合问题。为了对不确定的人造系统实施监控,在考虑事件的操作时间的基础上,利用带有发生事件概率分布函数的随机计时离散事件系统模型对系统建模。为了对这类随机系统实施监控,在传统方法中,采用控制任务的最大可控子语言设计控制器,不能体现系统模型的随机特性。本文提出利用软控制任务代替原控制任务的方法,使其超出原控制任务的概率在给定的容许度约束范围内。首先,通过在计时离散事件系统中定义计时事件的发生概率映射和发生费用函数,利用离散事件系统的逻辑特性,构造事件发生序列的期望费用函数,进而确立马氏决策过程的最优方程,建立软控制任务与期望费用函数之间的关系。然后,通过计算事件发生序列的费用值,提出利用有限费用值可以用来确定软控制任务,进而基于逻辑监控方法,确定最优监控器。最后,利用计算有限费用值的迭代过程,提出迭代算法,并给出了计算实例。     

基于赋时事件图的故障诊断

赋时事件图(TEG)是一类用于描述同步特性的重要的Petri网.本文提出并研究了基于赋时事件图的故障诊断问题.文中定义了两类系统故障类型:变迁失效(Invalidation)故障和变迁时间延迟(Time_lag)故障.基于事件图关联矩阵,通过研究变迁失效故障的可观测传播特性,引入了故障特征向量的概念.基于此,给出了失效故障的可诊断性的充分必要条件.对于时延故障,提出了一种基于变迁触发时间估计进行故障诊断的简单算法.并基于此算法,研究了时延故障的可诊断条件.     

Supervisory Control of a Class of Concurrent Discrete Event Systems Under Partial Observation

In this paper, we study supervisory control of a class of discrete event systems with simultaneous event occurrences, which we call concurrent discrete event systems, under partial observation. The behavior of the system is described by a language over the simultaneous event set. First, we prove that L_m(G)-closure, controllability, observability, and concurrent well-posedness of a specification language are necessary and sufficient conditions for the existence of a nonblocking supervisor. Next, we synthesize a supervisor that achieves the infimal closed, controllable, observable, and concurrently well-posed superlanguage of a specification language. Finally, we synthesize a supervisor that achieves a maximal closed, controllable, observable, and concurrently well-posed sublanguage of a closed specification language.     

Formulas for a class of controllable and observable sublanguages larger than the supremal controllable and normal sublanguage

In this paper, we give some new methods for synthesis of controllers of discrete event dynamical systems (DEDS) with partial event informations. Given a regular target language L, we construct some effective computable algorithms for computing the controllable and observable sublanguages of L. We show that any one of these controllable and observable sublanguages obtained by our algorithms is larger than the supremal controllable and normal sublanguage of L.     

A New Class of Supervisors for Timed Discrete Event Systems Under Partial Observation

Brandin and Wonham have developed a supervisory control framework for timed discrete event systems (TDESs) in order to deal with not only logical specifications but also temporal specifications. Lin and Wonham have extended this framework to the partial observation case, and presented necessary and sufficient conditions for the existence of a nonblocking supervisor under partial observation. In this paper, we define a new class of supervisors for TDESs under partial observation. We then present necessary and sufficient conditions for the existence of a nonblocking supervisor defined in this paper. These existence conditions of our supervisor are weaker than those of Lin and Wonham's supervisor. Note, however, that the price that must be paid to weaken the existence conditions is the higher computational cost. Moreover, given a closed regular language, we study computation of a sublanguage that satisfies the existence conditions of our supervisor. We present an algorithm for computing such a sublanguage larger than the supremal closed, controllable, and normal sublanguage.     

含不可观变迁事件图的状态估计器设计

针对基于事件图建模的离散事件系统中存在的不可观变迁的状态估计问题,本文提出前向、后 向可观路径的概念对其进行了详细分析,并给出一种估计器设计方法,用来根据关联矩阵行变换进行不可观 变迁状态的估计．分析了估计器的观测代价,在此基础上给出了寻找最优估计器的方法,并利用最优估计器 计算不可观变迁的状态估计范围．最后通过实例证明了该方法能够有效地进行不可观变迁的状态估计．     

<Emphasis Type="Italic">SetExp</Emphasis>: a method of transformation of timed automata into finite state automata

Real-time discrete event systems are discrete event systems with timing constraints, and can be modeled by timed automata. The latter are convenient for modeling real-time discrete event systems. However, due to their infinite state space, timed automata are not suitable for studying real-time discrete event systems. On the other hand, finite state automata, as the name suggests, are convenient for modeling and studying non-real time discrete event systems. To take into account the advantages of finite state automata, an approach for studying real-time discrete event systems is to transform, by abstraction, the timed automata modeling them into finite state automata which describe the same behaviors. Then, studies are performed on the finite state automata model by adapting methods designed for non real-time discrete event systems. In this paper, we present a method for transforming timed automata into special finite state automata called Set-Exp automata. The method, called SetExp, models the passing of time as real events in two types: Set events which correspond to resets with programming of clocks, and Exp events which correspond to the expiration of clocks. These events allow to express the timing constraints as events order constraints. SetExp limits the state space explosion problem in comparison to other transformation methods of timed automata, notably when the magnitude of the constants used to express the timing constraints are high. Moreover, SetExp is suitable, for example, in supervisory control and conformance testing of real-time discrete event systems.     

State feedback control of real-time discrete event systems with infinite states

In this paper, we study a state feedback supervisory control of timed discrete event systems (TDESs) with infinite number of states modelled as timed automata. To this end, we represent a timed automaton with infinite number of untimed states (called locations) by a finite set of conditional assignment statements. Predicates and predicate transformers are employed to finitely represent the behaviour and specification of a TDES with infinite number of locations. In addition, the notion of clock regions in timed automata is used to identify the reachable states of a TDES with an infinite time space. For a real-time specification described as a predicate, we present the controllability condition for the existence of a state feedback supervisor that restricts the behaviour of the controlled TDES within the specification.     

Distributed tracking control of uncertain mechanical systems with velocity constraints

This paper considers the leader‐following control problem of multiple mechanical systems with uncertainty and velocity constraints. So as to deal with the velocity constraints, a reduction procedure is applied to transform the model of each system to a cascaded system. With the aid of the cascade structure of each system and the properties of linear time‐varying systems, distributed robust feedback controllers are proposed such that the state of each follower system asymptotically converges to the state of a leader system with the aid of neighbors' information. So as to reduce the cost of the communication between systems, an event‐triggered leader‐following control problem is also considered, and event‐triggered distributed controllers are proposed. As an application of the proposed results, formation control of wheeled mobile robots is considered, and distributed controllers are obtained with the aid of the results in Theorems 1 and 2. Simulation results show the effectiveness of the proposed results. Copyright © 2017 John Wiley & Sons, Ltd.     

Model predictive control of P-time event graphs

This paper deals with model predictive control of discrete event systems modelled by P-time event graphs. First, the model is obtained by using the dater evolution model written in the standard algebra. Then, for the control law, we used the finite-horizon model predictive control. For the closed-loop control, we used the infinite-horizon model predictive control (IH-MPC). The latter is an approach that calculates static feedback gains which allows the stability of the closed-loop system while respecting the constraints on the control vector. The problem of IH-MPC is formulated as a linear convex programming subject to a linear matrix inequality problem. Finally, the proposed methodology is applied to a transportation system.     

Timed Discrete Event Control of Parallel Production Lines with Continuous Outputs

In this contribution we present an approach to formulate and solve certain scheduling tasks for hybrid systems using timed discrete event control methods. To demonstrate our approach, we consider a cyclically operated plant with parallel reactors using common resources and a continuous output. For this class of systems, we show how to pose the control problem within a discrete event framework by modelling system components as multirate timed automata. We propose a supervisory control strategy incorporating off-line optimisation to assure safety and nonconflicting use of resources. These properties have to be achieved in the presence of a class of bounded errors/disturbances and can be verified by applying formal methods.