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.     

Modeling and control of drug assignment for pharmaceutical cabinets using discrete event systems approaches

The public health sector, considered to be vital, especially in this pandemic crisis of COVID-19, requires automation and control of drug distribution in pharmacies commonly called: “Dispensing.” In this paper, we address the medication assignment problem for automated dispensing cabinets (ADCs). First, we use a network of conflicting timed event graphs (CTEGs), a class of timed Petri nets with shared resources, to model pharmaceutical cabinets. Second, we develop a new method for controlling CTEGs under mutual exclusion constraints (MECs) to solve the problem of drug assignment, using a control approach based on Min-Plus algebra. Finally, a case study of assigning drugs is given to illustrate the proposed methodology and show the efficiency of the developed control laws.     

Control of Petri nets subject to strict temporal constraints using Max-Plus algebra

In this paper, we treat the control problem of timed discrete event systems under temporal constraints. This type of constraint is very frequent in production systems, transportation network and in networked automation systems. Precisely, we are interested in the validation of strict temporal constraints imposed on the paths in a timed event graph (TEG) by using Max-Plus algebra. Not all the transitions of the considered TEG model are controllable, i.e. only the input transitions are controllable. An analytical approach for computing state feedback controllers is developed. Sufficient condition is given for the existence of causal control laws satisfying the temporal constraints. In the first, a TEG with observable transitions is considered. Then, the proposed approach is extended to the partially observable TEG. The synthesised feedback can be interpreted by places of control connected to the TEG to guarantee the respect of the time constraints. The proposed method is illustrated in the assembly system example.     

一类离散事件系统的监控器综合

前向无同步前向无冲突网是每个变迁有且只有一个输入库所并且每个库所最多有一个输入变迁的受限Petri网.针对不可控影响子网为前向无同步前向无冲突网的广义互斥约束,显式地给出了最大允许控制策略的计算方法.并用一个例子给予了说明.     

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.     

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。     

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.     

Diagnosability of discrete event systems and its applications

As man-made systems become more and more complex, diagnostics of component failures is no longer an easy task that can be performed based on experience and intuition. Therefore, it is important to develop a systematic approach to diagnostic problems. Diagnostics can be done either on-line or off-line. By on-line diagnostics, we mean diagnostics performed while the system to be diagnosed is in normal operation. On the other hand, in off-line diagnostics, the system is not in normal operation. We will study both on-line and off-line diagnostics in this paper and identify main features and differences of these two types of diagnostics. We will also introduce the concept of diagnosability and study its properties, all in the framework of discrete event systems. This study is motivated by diagnostic problems in the automotive industry and we will emphasize its applications.     

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.     

Fault detection and isolation in manufacturing systems with an identified discrete event model

In this article a generic method for fault detection and isolation (FDI) in manufacturing systems considered as discrete event systems (DES) is presented. The method uses an identified model of the closed-loop of plant and controller built on the basis of observed fault-free system behaviour. An identification algorithm known from literature is used to determine the fault detection model in form of a non-deterministic automaton. New results of how to parameterise this algorithm are reported. To assess the fault detection capability of an identified automaton, probabilistic measures are proposed. For fault isolation, the concept of residuals adapted for DES is used by defining appropriate set operations representing generic fault symptoms. The method is applied to a case study system.     

Supervisory control of discrete event systems with state-dependent controllability

This article studies the supervisory control problem of discrete event systems (DES) with state-dependent controllability. The new problem is given with the background of operating systems where the processes and the interrupt service routines (ISR) are supervised and coordinated. The new model is novel because the controllability of an event is changeable in the lifetime of system evolution, and dependent on the system state. Two fundamental problems are concerned with the new model: supervisor existence problem and supervisor synthesis problem. We derive a necessary and sufficient condition for the existence of the supervisor, and introduce an algorithm to synthesise the supremal supervisor in a given specification. With the background of process and ISR management in operating systems, some examples are given to show how the new model can be applied to practical computing.     

On-line control of partially observed discrete event systems

It is well known that the design of supervisors for partially observed discrete-event systems is an NP-complete problem and hence computationally impractical. Furthermore, optimal supervisors for partially observed systems do not generally exist. Hence, the best supervisors that can be designed directly for operation under partial observation are the ones that generate the supremal normal (and controllable) sublanguage. In the present paper we show that a standard procedure exists by which any supervisor that has been designed for operation under full observation, can be modified to operate under partial observation. When the procedure is used to modify the optimal full-observation supervisor (i.e., the one that generates the supremal controllable language), the resultant modified supervisor is at least as efficient as the best one that can be designed directly (that generates the supremal normal sublanguage). The supervisor modification algorithm can be carried out on-line with linear computational complexity and hence makes the control under partial observation a computationally feasible procedure.     

分布式多机器人运动控制的离散事件系统方法

传统多机器人系统的运动控制主要依赖于机器人的动力学方程或运动学方程,通过求解微分方程组来获得机器人的输入控制信号.随着系统中机器人数量的增加和运行环境的复杂化,动力学方程很难描述多机器人系统的运动行为,且无法很好地解决诸如死锁等逻辑故障.本文简略综述了国内外的研究现状,重点介绍笔者所在研究组开展的关于离散事件系统方法在多机器人运动控制方面的应用性研究工作.其动机在于:1)基于离散事件系统方法的运动控制能够有效地解决系统运行过程中产生的诸如死锁等逻辑故障.首先,利用离散事件系统模型对多机器人系统的运动进行建模,从而降低计算复杂性;其次,基于所得离散事件系统模型,设计分布式安全运动控制算法,使各个机器人可以自主地、无碰撞地、无死锁地运动;设计分布式鲁棒运动控制算法,使得失效的机器人对系统的影响最小.2)基于离散事件系统方法的运动控制策略可以结合传统的基于运动学方程的运动控制方法,从而使系统不但能够避免顶层的逻辑故障,而且能够确定机器人执行器的输入信号.     

受扰线性离散系统的前馈2反馈最优控制

研究具有已知动态特性但未知初始条件的持续外界扰动的线性离散系统最优控制问题。给出了前馈一反馈最优控制律的存在唯一性条件，并提出了最优控制律的设计算法．通过降维扰动观测器解决了前馈一反馈最优控制律的物理不可实现问题．对近海结构物振动控制的实例仿真表明，该设计算法易于实现，在抑制外部持续扰动和鲁棒性方面优于经典的状态反馈最优控制。     

Control of large scale discrete event systems: Task allocation and coordination

To control a large scale discrete event system, decentralized control and hierarchical control can be used, where several local supervisors are used to control events in local sites and a coordinator is used to coordinate the local supervisors. Two important problems that need to be solved in such a control architecture are task allocation and coordination. That is, how to allocate tasks to the supervisors, and how to coordinate those tasks. We propose and solve a task allocation problem of assigning tasks to the local supervisors and a minimal intervention problem of coordinating tasks so that the intervention by the coordinator is minimal.     

离散事件系统的混合分散监控

研究了混合信息下的分散监控综合问题.首先提出δ-可观察(hδ-可观察)可控闭语言是(状态部分可观察下)状态反馈综合解存在的充要条件,并由此得到n-联合可观察、可控闭的系统约束是保证混合分散监控器存在的充要条件,进而得到纯分散监控器(控制器)存在的充要条件为n-可观察(n-hδ-可观察)可控闭语言被满足.最后,又通过研究系统约束与混合约束的关系,提出混合分散监控器存在的充分条件是可观察、可控闭语言与可观察可控谓词被满足.     

非确定型离散事件系统双模拟控制的实现

近年来,双模拟等价关系与离散事件系统监控理论相结合的研究引起了国内外许多学者的广泛关注.本文针对作者在前期工作中提出的非确定型离散事件系统的双模拟控制机制,进一步探讨其实现问题.利用投影映射对系统规范说明语言进行等价类划分,构造了一棵计算树,得到了一个判断规范说明是否具有基于模拟关系可观性的多项式算法,证明了双模拟控制机制是多项式时间算法可实现的.同时,通过对控制器配备具有存储和判断功能的模拟关系识别器,阐述了这种双模拟控制机制是物理可实现的.     

On optimal control of a class of partially observed discrete event systems

We are interested in a new class of optimal control problems for discrete event systems. We adopt the formalism of supervisory control theory (Proc. IEEE 77(1) (1989) 81) and model the system as a finite state machine (FSM). Our control problem is characterized by the presence of uncontrollable as well as unobservable events, the notion of occurrence and control costs for events and a worst-case objective function. We first derive an observer for the partially unobservable FSM, which allows us to construct an approximation of the unobservable trajectory costs. We then define the performance measure on this observer rather than on the original FSM itself. We then use the algorithm presented in Sengupta and Lafortune (SIAM J. Control Optim. 36(2) (1998)) to synthesize an optimal submachine of the C-observer. This submachine leads to the desired supervisor for the system.     

离散事件系统的混合可靠分散监控

在研究基于混合信息的分散监控时,由于部分监控器与部分控制器发生失败,故提出了一种新型的混合可靠分散监控问题.通过修改局部可控事件集与不可控事件集,提出新的可控语言与可靠联合可观察语言定义,进而得到混合可靠分散监控器存在的充分必要条件就是整体约束语言是可靠联合可观察,可控闭的.之后,又通过研究整体约束与混合子约束之间的关系,给出了判别混合可靠分散监控器存在的一个充分条件,即混合子约束分别满足基于谓词的可观察,可控性与基于语言的联合可观察,可控封闭性.     

On tolerable and desirable behaviors in supervisory control of discrete event systems

We formulate and solve a new supervisory control problem for discrete event systems. The objective is to design a logical controller—or supervisor—such that the discrete event system satisfies a given set of requirements that involve event ordering. The controller must deal with a limited amount of controllability in the form of uncontrollable events. Our problem formulation considers that the requirements for the behavior (i.e., set of traces) of the controlled system are specified in terms of a desired behavior and a larger tolerated behavior. Due to the uncontrollable events, one may wish to tolerate behavior that sometimes exceeds the ideal desired behavior if overall this results in achieving more of the desired behavior. The general solution of our problem is completely characterized. The nonblocking solution is also analyzed in detail. This solution requires the study of a new class of controllable languages. Several results are proved about this class of languages. Algorithms to compute certain languages of interest within this class are also presented.Research supported in part by the National Science Foundation under grants ECS-8707671, ECS-9057967, and ECS-9008947.