State-Based Control of Fuzzy Discrete Event Systems

To effectively represent possibility arising from states and dynamics of a system, fuzzy discrete event systems as a generalization of conventional discrete event systems have been introduced recently. Supervisory control theory based on event feedback has been well established for such systems. Noting that the system state description, from the viewpoint of specification, seems more convenient, we investigate the state-based control of fuzzy discrete event systems in this paper. We first present an approach to finding all fuzzy states that are reachable by controlling the system. After introducing the notion of controllability for fuzzy states, we then provide a necessary and sufficient condition for a set of fuzzy states to be controllable. We also find that event-based control and state-based control are not equivalent and further discuss the relationship between them. Finally, we examine the possibility of driving a fuzzy discrete event system under control from a given initial state to a prescribed set of fuzzy states and then keeping it there indefinitely.Comment: 14 double column pages; 4 figures; to be published in the IEEE Transactions on Systems, Man, and Cybernetics--Part B: Cybernetic

Detectability Of Fuzzy Discrete Event Systems

Dynamic systems that can be modeled in terms of discrete states and a synchronous events are known as discrete event systems (DES). A DES is defined in terms of states, events, transition dynamics, and initial state. Knowing the system’s state is crucial in many applications for certain actions (events) to be taken. A DES system is considered a fuzzy discrete event system (FDES) if its states and events are vague in nature; for such systems, the system can be in more than one state at the same time with different degrees of possibility (membership). In this research we introduce a fuzzy discrete event system with constraints (FDESwC) and investigate its detectabilities. This research aims to address the gap in previous studies and extend existing definitions of detectability of DES to include the detectability in systems with substantial vagueness such as FDES. These definitions are first reformulated to introduce N-detectability for DES, which are further extended to define four main types of detectabilities for FDES: strong N-detectability, (weak) N-detectability, strong periodic N-detectability, and (weak) periodic N-detectability. We first partition the FDES into trajectories of a length dictated by the depth of the event’s string (length of the event sequence); each trajectory consists of a number of nodes, which are further investigated for detectability by examining them against the newly introduced certainty criterion. Matrix computation algorithms and fuzzy logic operations are adopted to calculate the state estimates based on the current state and the occurring events. Vehicle dynamics control example is used to demonstrate the practical aspect of developed theorems in real-world applications

Modeling and control of operator functional state in a unified framework of fuzzy inference petri nets

Background and objective: In human-machine (HM) hybrid control systems, human operator and machine cooperate to achieve the control objectives. To enhance the overall HM system performance, the discrete manual control task-load by the operator must be dynamically allocated in accordance with continuous-time fluctuation of psychophysiological functional status of the operator, so-called operator functional state (OFS). The behavior of the HM system is hybrid in nature due to the co-existence of discrete task-load (control) variable and continuous operator performance (system output) variable. Methods: Petri net is an effective tool for modeling discrete event systems, but for hybrid system involving discrete dynamics, generally Petri net model has to be extended. Instead of using different tools to represent continuous and discrete components of a hybrid system, this paper proposed a method of fuzzy inference Petri nets (FIPN) to represent the HM hybrid system comprising a Mamdani-type fuzzy model of OFS and a logical switching controller in a unified framework, in which the task-load level is dynamically reallocated between the operator and machine based on the model-predicted OFS. Furthermore, this paper used a multi-model approach to predict the operator performance based on three electroencephalographic (EEG) input variables (features) via the Wang-Mendel (WM) fuzzy modeling method. The membership function parameters of fuzzy OFS model for each experimental participant were optimized using artificial bee colony (ABC) evolutionary algorithm. Three performance indices, RMSE, MRE, and EPR, were computed to evaluate the overall modeling accuracy. Results: Experiment data from six participants are analyzed. The results show that the proposed method (FIPN with adaptive task allocation) yields lower breakdown rate (from 14.8% to 3.27%) and higher human performance (from 90.30% to 91.99%). Conclusion: The simulation results of the FIPN-based adaptive HM (AHM) system on six experimental participants demonstrate that the FIPN framework provides an effective way to model and regulate/optimize the OFS in HM hybrid systems composed of continuous-time OFS model and discrete-event switching controller

Diagnosability of Fuzzy Discrete Event Systems

In order to more effectively cope with the real-world problems of vagueness, {\it fuzzy discrete event systems} (FDESs) were proposed recently, and the supervisory control theory of FDESs was developed. In view of the importance of failure diagnosis, in this paper, we present an approach of the failure diagnosis in the framework of FDESs. More specifically: (1) We formalize the definition of diagnosability for FDESs, in which the observable set and failure set of events are {\it fuzzy}, that is, each event has certain degree to be observable and unobservable, and, also, each event may possess different possibility of failure occurring. (2) Through the construction of observability-based diagnosers of FDESs, we investigate its some basic properties. In particular, we present a necessary and sufficient condition for diagnosability of FDESs. (3) Some examples serving to illuminate the applications of the diagnosability of FDESs are described. To conclude, some related issues are raised for further consideration.Comment: 14 pages; revisions have been mad

Analysis, filtering, and control for Takagi-Sugeno fuzzy models in networked systems

Copyright © 2015 Sunjie Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.The fuzzy logic theory has been proven to be effective in dealing with various nonlinear systems and has a great success in industry applications. Among different kinds of models for fuzzy systems, the so-called Takagi-Sugeno (T-S) fuzzy model has been quite popular due to its convenient and simple dynamic structure as well as its capability of approximating any smooth nonlinear function to any specified accuracy within any compact set. In terms of such a model, the performance analysis and the design of controllers and filters play important roles in the research of fuzzy systems. In this paper, we aim to survey some recent advances on the T-S fuzzy control and filtering problems with various network-induced phenomena. The network-induced phenomena under consideration mainly include communication delays, packet dropouts, signal quantization, and randomly occurring uncertainties (ROUs). With such network-induced phenomena, the developments on T-S fuzzy control and filtering issues are reviewed in detail. In addition, some latest results on this topic are highlighted. In the end, conclusions are drawn and some possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grants 61134009, 61329301, 11301118 and 61174136, the Natural Science Foundation of Jiangsu Province of China under Grant BK20130017, the Fundamental Research Funds for the Central Universities of China under Grant CUSF-DH-D-2013061, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Supervisory Control of Fuzzy Discrete Event Systems

In order to cope with situations in which a plant's dynamics are not precisely known, we consider the problem of supervisory control for a class of discrete event systems modelled by fuzzy automata. The behavior of such discrete event systems is described by fuzzy languages; the supervisors are event feedback and can disable only controllable events with any degree. The concept of discrete event system controllability is thus extended by incorporating fuzziness. In this new sense, we present a necessary and sufficient condition for a fuzzy language to be controllable. We also study the supremal controllable fuzzy sublanguage and the infimal controllable fuzzy superlanguage when a given pre-specified desired fuzzy language is uncontrollable. Our framework generalizes that of Ramadge-Wonham and reduces to Ramadge-Wonham framework when membership grades in all fuzzy languages must be either 0 or 1. The theoretical development is accompanied by illustrative numerical examples.Comment: 12 pages, 2 figure

Observability and Decentralized Control of Fuzzy Discrete Event Systems

Fuzzy discrete event systems as a generalization of (crisp) discrete event systems have been introduced in order that it is possible to effectively represent uncertainty, imprecision, and vagueness arising from the dynamic of systems. A fuzzy discrete event system has been modelled by a fuzzy automaton; its behavior is described in terms of the fuzzy language generated by the automaton. In this paper, we are concerned with the supervisory control problem for fuzzy discrete event systems with partial observation. Observability, normality, and co-observability of crisp languages are extended to fuzzy languages. It is shown that the observability, together with controllability, of the desired fuzzy language is a necessary and sufficient condition for the existence of a partially observable fuzzy supervisor. When a decentralized solution is desired, it is proved that there exist local fuzzy supervisors if and only if the fuzzy language to be synthesized is controllable and co-observable. Moreover, the infimal controllable and observable fuzzy superlanguage, and the supremal controllable and normal fuzzy sublanguage are also discussed. Simple examples are provided to illustrate the theoretical development.Comment: 14 pages, 1 figure. to be published in the IEEE Transactions on Fuzzy System

Supervisory Control of Fuzzy Discrete Event Systems: A Formal Approach

Fuzzy {\it discrete event systems} (DESs) were proposed recently by Lin and Ying [19], which may better cope with the real-world problems with fuzziness, impreciseness, and subjectivity such as those in biomedicine. As a continuation of [19], in this paper we further develop fuzzy DESs by dealing with supervisory control of fuzzy DESs. More specifically, (i) we reformulate the parallel composition of crisp DESs, and then define the parallel composition of fuzzy DESs that is equivalent to that in [19]; {\it max-product} and {\it max-min} automata for modeling fuzzy DESs are considered; (ii) we deal with a number of fundamental problems regarding supervisory control of fuzzy DESs, particularly demonstrate controllability theorem and nonblocking controllability theorem of fuzzy DESs, and thus present the conditions for the existence of supervisors in fuzzy DESs; (iii) we analyze the complexity for presenting a uniform criterion to test the fuzzy controllability condition of fuzzy DESs modeled by max-product automata; in particular, we present in detail a general computing method for checking whether or not the fuzzy controllability condition holds, if max-min automata are used to model fuzzy DESs, and by means of this method we can search for all possible fuzzy states reachable from initial fuzzy state in max-min automata; also, we introduce the fuzzy $n$-controllability condition for some practical problems; (iv) a number of examples serving to illustrate the applications of the derived results and methods are described; some basic properties related to supervisory control of fuzzy DESs are investigated. To conclude, some related issues are raised for further consideration