The challenge of modelling supervisory systems using fuzzy cognitive maps

This paper examines fuzzy cognitive map (FCM) theory and its use in supervisory control systems. An FCM is a graph used to depict cause and effect between concepts that stand for the states and variables of the system. An FCM represents the whole system in a symbolic manner, just as humans have stored the operation of the system in their brains, thus it is possible to help man's intention for more intelligent and autonomous systems. FCM representation, construction and a mathematical model are examined; a generic system is proposed and the implementation of FCM in a process control problem is illustrated and a model for supervisors of manufacturing systems is discussed. Although an FCM seems to be a simple model of system behaviour, it appears to be a powerful and effective tool describing the behaviour of a system and representing the accumulated knowledge of a system.     

Real-time preemptive scheduling of sporadic tasks based on supervisory control of discrete event systems

This paper presents a preemptive scheduling scheme for real-time systems with sporadic tasks based on the supervisory control theory of discrete event systems. In particular, we present a systematic method of computing a schedulable language that includes all achievable sequences that meet the given deadlines of accepted sporadic tasks. A supervisor that achieves the schedulable language corresponds to a scheduler that can secure the deadlines of all accepted tasks. We further show that the schedulable language includes the decisions on whether a scheduler accepts or rejects a newly arrived sporadic task.     

A fuzzy hierarchical reinforcement learning based scheduling method for semiconductor wafer manufacturing systems

Scheduling semiconductor wafer manufacturing systems has been viewed as one of the most challenging optimization problems owing to the complicated constraints, and dynamic system environment. This paper proposes a fuzzy hierarchical reinforcement learning (FHRL) approach to schedule a SWFS, which controls the cycle time (CT) of each wafer lot to improve on-time delivery by adjusting the priority of each wafer lot. To cope with the layer correlation and wafer correlation of CT due to the re-entrant process constraint, a hierarchical model is presented with a recurrent reinforcement learning (RL) unit in each layer to control the corresponding sub-CT of each integrated circuit layer. In each RL unit, a fuzzy reward calculator is designed to reduce the impact of uncertainty of expected finishing time caused by the rematching of a lot to a delivery batch. The results demonstrate that the mean deviation (MD) between the actual and expected completion time of wafer lots under the scheduling of the FHRL approach is only about 30 % of the compared methods in the whole SWFS.     

Mutually nonblocking supervisory control of discrete event systems

A single maximally permissive and nonblocking supervisor to simultaneously fulfill several marked specifications pertaining to a single plant is investigated. Given a plant G and two marked specification languages K₁ and K₂, a supervisor S is said to be (K₁,K₂)-mutually nonblocking if (for i,j=1,2)

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. This means that when the closed-loop system marks a trace of K_i, then it is always able to continue to a trace of K_j, also marked in the closed-loop system. Thus, the controlled system can execute traces within one specification while always being able to continue a trace of the other and hence not blocking the other specification. A complete, globally nonblocking and (K₁,K₂)-mutually nonblocking supervisor such that L_m(G || S)K₁K₂ exists if and only if there exists a controllable mutually nonblocking sublanguage of the union of the specifications. There does exist a supremal such language. Furthermore, in the case that each specification is nonconflicting with respect to the prefix-closure of the other, this supremal language can be calculated by expressing it as the union of the supremal prefix-bounded sublanguages of the respective specifications. Finally, we show that the multiply nonblocking supervision of Thistle, Malhame, Hoang and Lafortune ((1997). Internal Report, Dept. de genie electrique et de genie informatique, Ecole Polytechnique de Montreal, Canada) is equivalent to globally and mutually nonblocking supervision.     

Modular supervisory control of discrete-event systems

A modular approach to the supervisory control of a class of discrete-event systems is formulated, and illustrated with an example. Discrete-event systems are modeled by automata together with a mechanism for enabling and disabling a subset of state transitions. The basic problem of interest is to ensure by appropriate supervision that the closed loop behavior of the system lies within a given legal behavior. Assuming this behavior can be decomposed into an intersection of component restrictions, we determine conditions under which it is possible to synthesize the appropriate control in a modular fashion. The work of this author was supported by NSERC (Canada) under Grant No. A-7399. The work of this author was supported by the National Science Foundation through Grant No. ECS-8504584.     

Grid automata and supervisory control of dense real-time discrete event systems

We present a generalization of the classical supervisory control theory for discrete event systems to a setting of dense real-time systems modeled by Alur and Dill timed automata. The main problem involved is that in general the state space of a timed automaton is (uncountably) infinite. The solution is to reduce the dense time transition system to an appropriate finite discrete subautomaton, the grid automaton, which contains enough information to deal with the timed supervisory control problem (TSCP). The plant and the specifications region graphs are sampled for a granularity defined in a way that each state has an outgoing transition labeled with the same time amount. We redefine the controllability concept in the context of grid automata, and we provide necessary and sufficient solvability conditions under which the optimal solution to centralized supervisory control problems in timed discrete event systems under full observation can be obtained. The enhanced setting admits subsystem composition and the concept of forcible event. A simple example illustrates how the new method can be used to solve the TSCP.     

Energy-to-peak control for a class of discrete stochastic fuzzy systems with time-delay

This paper considers the problem of stochastic stabilization and energy-to-peak control for a class of discrete stochastic fuzzy systems with interval time-delays. The objective is to design a state feedback controller suchthat the closed-loop system is stochastic stable and satisfies energy-to-peak performance. Based on the idea of interval partitioning, some new sufficient conditions are presented in LMI.     

Design, implementation and testing of an intelligent knowledge-based system for the supervisory control of a hot rolling mill

This paper describes the design, implementation and testing of an intelligent knowledge-based supervisory control (IKBSC) system for a hot rolling mill process. A novel architecture is used to integrate an expert system with an existing supervisory control system and a new optimization methodology for scheduling the soaking pits in which the material is heated prior to rolling. The resulting IKBSC system was applied to an aluminium hot rolling mill process to improve the shape quality of low-gauge plate and to optimise the use of the soaking pits to reduce energy consumption. The results from the trials demonstrate the advantages to be gained from the IKBSC system that integrates knowledge contained within data, plant and human resources with existing model-based systems.     

Countering the loss of extended vigilance in supervisory control using a fuzzy logic model

When an operator first detects unusual and/or infrequent or irregular signals in a system, the operator does not need to take any action, but must increase his/her level of attention and be alert for any more serious signals that may confirm a problem with the system. This is referred to as extended vigilance. The purpose of this study was to construct a fuzzy vigilance-measuring model for countering the loss of extended vigilance. The model extends two-valued logic (“Yes” or “No”) to multi-valued logic through fuzzy sets. Then a fuzzy logic alarm was developed by the model for combating the extended vigilance decrement. The first experiment compared the effect of the fuzzy measuring model with signal detection theory (SDT) and discussed the relationship between preliminary and extended vigilance for a simulated feed-water monitoring system. The results indicated that the sensitivity of the fuzzy vigilance-measuring model is better than index d′ and β, and that the preliminary vigilance significantly influences the extended vigilance. The second experiment verified the effect of the fuzzy logic alarm. The results indicated that the effect of the fuzzy logic alarm for combating the extended vigilance decrement is significant. When the preliminary vigilance is poor, an appropriate alarm will improve the extended vigilance. However, if the preliminary vigilance is very poor, the improvement of the extended vigilance will be limited.Relevance to industry: The extended vigilance is a new and important issue in human performance problems in industry, particularly in such areas as air-traffic control, industrial inspection and power plant monitor. The measuring model of vigilance could be applied to develop an alarm for promoting supervisory performance of human and human–machine detectors.     

Multi-level hierarchical interface-based supervisory control

Hierarchical Interface-Based Supervisory Control employs interfaces that allow properties of a monolithic system to be verified through local analysis. By avoiding the need to verify properties globally, significant computational savings can be achieved. In this paper we provide local requirements for a multi-level architecture employing command-pair type interfaces. This multi-level architecture allows for a greater reduction in complexity and improved reconfigurability over the two-level case that has been previously studied since it allows the global system to be partitioned into smaller modules. This paper also provides results for synthesizing supervisors in the multi-level architecture that are locally maximally permissive with respect to a given specification and set of interfaces.     

离散T-S模糊广义系统的H∞控制

研究了离散T-S模糊广义系统的H_∞控制问题. 首先引入辅助矩阵变量得到新的容许性条件, 解决了由于矩阵P的不定性, 无法运用Schur补引理处理非线性Lyapunov不等式的问题, 进而得到严格不等式表示的H_∞控制条件.基于模糊Lyapunov函数方法, 分别研究了状态反馈控制器、静态输出反馈控制器、动态输出反馈控制器的构造方法. 所得结论可推广到系统具有范数有界不确定性的情况. 最后通过算例验证方法的有效性.     

Multi-objective supervisory flow control based on fuzzy interval arithmetic: Application for scheduling of manufacturing systems

Complex production systems can produce more than one part type under multiple and possibly conflicting objectives. This paper considers the design of the multiple objective real-time scheduling problem of a multiple-part-type production system. Based on fuzzy control theory and fuzzy arithmetic intervals, distributed and supervised continuous-flow control architecture has been proposed. The objective is to balance the production process by adjusting the continuous production rates of the machines on the basis of the average behaviour. The supervisory control aims to maintain the overall performance within acceptable limits. In the proposed approach, the problem of a real-time scheduling of jobs is considered at the shop-floor level. In this case, the actual dispatching times are determined from the continuous production rates through a discretisation procedure. To deal with conflicts between jobs at a shared machine, a decision for the actual part to be processed is taken using some criterions which represent a measure of the job’s priority. A case study demonstrates the efficiency of the proposed control approach.     

Diagnosability of fuzzy discrete event systems

In this paper, discrete event systems (DESs) are reformulated as fuzzy discrete event systems (FDESs) and fuzzy discrete event dynamical systems (FDEDSs). These frameworks include fuzzy states, events and IF-THEN rules. In these frameworks, all events occur at the same time with different membership degrees. Fuzzy states and events have been introduced to describe uncertainties that occur often in practical problems, such as fault diagnosis applications. To measure a diagnoser’s fault discrimination ability, a fuzzy diagnosability degree is proposed. If the diagnosability of the degree of the system yields one a diagnoser can be implemented to identify all possible fault types related to a system. For any degree less than one, researchers should not devote their time to distinguish all possible fault types correctly. Thus, two different diagnosability definitions FDEDS and FDES are introduced. Due to the specialized fuzzy rule-base embedded in the FDEDS, it is capable of representing a class of non-linear dynamic system. Computationally speaking, the framework of diagnosability of the FDEDS is structurally similar to the framework of diagnosability of a non-linear system. The crisp DES diagnosability has been turned into the term fuzzy diagnosability for the FDES. The newly proposed diagnosability definition allows us to define a degree of diagnosability in a class of non-linear systems. In addition, a simple fuzzy diagnosability checking method is introduced and some numerical examples are provided to illustrate this theoretical development. Finally, the potential applications of the proposed method are discussed.     

一类不确定离散切换模糊时滞系统的鲁棒非脆弱控制

针对一类不确定离散切换模糊时滞系统,研究了在控制器增益存在摄动情况下的稳定性问题.利用切换技术和多Lyapunov函数方法,并以矩阵不等式形式给出了非脆弱状态反馈控制器存在的充分条件和切换律设计.最后通过数值仿真算例验证了设计方法的有效性和可行性.     

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.     

Chattering-free fuzzy variable structure control for multivariable nonlinear systems

In this paper, a fuzzy logic controller (FLC) based variable structure control (VSC) with guaranteed stability for multivariable systems is presented. It is aimed at obtaining an improved performance of nonlinear multivariable systems. The main contribution of this work is firstly developing a generic matrix formulation of the FLC-VSC algorithm for nonlinear multivariable systems, with a special attention to non-zero final state. Secondly, ensuring the global stability of the controlled system. The multivariable nonlinear system is represented by T-S fuzzy model. The identification of the T-S model parameters has been improved using the well known weighting parameters approach to optimize local and global approximation and modeling capability of T-S fuzzy model. The main problem encountered is that T-S identification method cannot be applied when the membership functions (MFs) are overlapped by pairs. This in turn restricts the application of the T-S method because this type of membership function has been widely used in control applications. In order to overcome the chattering problem a switching function is added as an additional fuzzy variable and will be introduced in the premise part of the fuzzy rules together with the state variables. A two-link robot system and a mixing thermal system are chosen to evaluate the robustness, effectiveness, accuracy and remarkable performance of proposed FLC-VSC method.     

Simulating continuous fuzzy systems

In previous studies we concentrated on utilizing crisp, numeric simulation to produce discrete event fuzzy systems simulations. Then we extended this research to the simulation of continuous fuzzy systems models. In this study, we continue our study of continuous fuzzy systems using crisp continuous simulation. Consider a crisp continuous system whose process of evolution depends on differential equations. Such a system contains a number of parameters that must be estimated. Usually point estimates are computed and used in the model. However, these point estimates typically have uncertainty associated with them. We propose to incorporate uncertainty by using fuzzy numbers as estimates of these unknown parameters. Fuzzy parameters convert the crisp system into a fuzzy system. Trajectories describing the behavior of the system become fuzzy curves. We will employ crisp continuous simulation to estimate these fuzzy trajectories. Three examples are discussed.     

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.     

Petri-net-based robust supervisory control of automated manufacturing systems

Supervisory control that ensures deadlock-free and nonblocking operation has been an active research area of manufacturing engineering. So far, most of deadlock control policies in the existing literature assume that allocated resources are reliable. Additionally, a large number of methods are for systems of simple sequential processes with resources (S³PRs), where a part uses only one copy of one resource at each processing step. In contrast, we investigate the automated manufacturing systems (AMSs) that can be modeled by a class of Petri nets, namely S^*PUR. S^*PUR is a generalization of the S^*PR Petri net model, while S^*PR is a superclass of S³PR. This work addresses the robust supervision for deadlock avoidance in S^*PUR. Specifically, we take into account unreliable resources that may break down while working or being in idle, and the considered AMSs allow the use of multiple copies of different resources per operation stage. Our objective is to control the system so that: 1) when there are breakdowns, the system can continue producing parts of some types whose production does not need any failed resources; and 2) given the correction of all faults, it is possible to complete all the on-going part instances remaining in the system. We illustrate the characteristics of a desired supervisor through several examples, define the corresponding properties of robustness, and develop a control policy that satisfies such properties.     

Managing quality-of-control and requirement-of-bandwidth in networked control systems via fuzzy bandwidth scheduling

There is an unavoidable tradeoff between the control performance and the quality of service in networked control systems with resource constraints. To address the impact of network resources availability on requirement of bandwidth (RoB) and quality of control (QoC), an intelligent control approach to dynamic bandwidth management, namely fuzzy bandwidth management, is proposed based on fuzzy logic control technique. In order to guarantee the system’s stability, the lower and upper bound of the assignable bandwidth are evaluated in terms of linear matrix inequalities and the resource constraints, respectively. In addition, the normalizable criterions of QoC and RoB are also defined, which can estimate the performance of the whole networked control systems. Preliminary simulations are carried out to highlight the merits of the proposed approach. It is argued that the proposed approach can save significant bandwidth and simultaneously improve overall control performance in comparison with the fixed bandwidth allocation and optimal bandwidth allocation. Recommended by Editorial Board member Young Il Lee under the direction of Editor Young-Hoon Joo. This work was supported by the National Natural Science Foundation of China under Grants 60573123, 60872057, and by the Zhejiang Provincial Natural Science Foundation of China under grant Y107293. Zuxin Li received the B.Eng. degree from Zhejiang University of Technology, China, in 1995, the M.Sc. (Eng.) degree from Yunnan Univer-sity, China, in 2002, and the Ph.D. degree from Zhejiang University of Technology, China, in 2008. He is currently an Associate Professor in the School of Information Engineering, Huzhou Teachers College, China. His research interests include networked control systems and intelligent control. Wanliang Wang received the Ph.D. degree from Tongji University, China, in 2001. He is currently a Professor in Zhejiang University of Technology, China. His research interests include computer control, computer net, CMIS, and production scheduling. Yunliang Jiang received the B.S. degree in Mathematics from Zhejiang Normal University in 1989, and the M.E. and Ph.D. degrees in Computer Science and Technology from Zhejiang University, Hangzhou, China. He is currently a Professor in the School of Information Engineering, Huzhou Teachers College, China. His research interests include information fusion, artificial intelligence, and geographic information system.