Analysis and control of fuzzy discrete event systems using bisimulation equivalence

In order to make it possible to effectively represent deterministic uncertainties and vagueness as well as the human subjective observation and judgement inherent to many real-world problems, especially those in biomedicine, we introduce, in this paper, fuzzy states and fuzzy events and generalize (crisp) discrete event systems (DES) to fuzzy DES. The largely graph-based current framework of the crisp DES is unsuitable for the expansion, and we have thus reformulated it using state vectors and event transition matrices which can be extended to fuzzy vectors and matrices by allowing their elements to take values between 0 and 1. To measure information related to fuzzy DES, we generalize the crisp DES observability. The new observability allows one to determine whether or not the system output observed is sufficient for decision making. Finally, we extend the optimal control of DES to fuzzy DES. The new fuzzy DES theory is consistent with the existing theory, both at the conceptual and the computation levels, in that the former contains the latter as a special case when the memberships must be either 0 or 1. Numerical examples are provided to illustrate the theoretical development.

We investigate modeling and control of probabilistic fuzzy discrete event systems (PFDES). PFDES is a new type of fuzzy discrete event systems. It allows the use of probabilities to describe the chances of occurrences of different events. Our new model for PFDES consists of a fuzzy automaton and a crisp automaton that specifies what sequences of events can occur and their probabilities of occurrences. Based on the new model, optimal control is designed using an on-line and limited lookahead method. Control is calculated one step at a time, after an occurrence of an event. At each step, a lookahead window of $N$ events is constructed. The performance measures for all states in the window are determined, which is a function of fuzzy states. Control is calculated to maximize the expected performance measure after the occurrences of $N$ events. To reduce computational complexity, a “dynamic-programming” approach is proposed. We prove that the control obtained is optimal. Examples are given in the paper to illustrate the results.

This paper is a reply to comments on "State-feedback control of fuzzy discrete-event systems" by Yongzhi Cao et l., (2011) for pointing out an error in our paper "State-feedback control of fuzzy discrete event systems" (June 2010). The error is caused by the situation in which a state-feedback control may generate a set of states while not allowing some transitions in the set of states generated. Since this situation is inconsistent and does not make sense for any good control, one shall not allow it to happen. When we formulated the problem in our original paper, we intended to exclude this situation. Nevertheless, somehow, we overlooked the issue and did not make an explicit assumption. To correct the error, we now add an assumption to explicitly exclude this situation.

Diagnosability of fuzzy discrete event systems

The non-linear, asynchronous and uncertain nature must be considered in the control of air-conditioning (AC) system as the AC systems tend to become large-scale and more complicated. In this paper, a fuzzy discrete event systems (FDES) is introduced into the AC control. A fuzzy automaton for AC system is given. A new modelling and control method is then proposed. Cost and effectiveness functions are optimised. The simulation results show that the optimal control can be better achieved using the FDES for the AC systems.

We study supervisory control for enforcing nondeterministic specifications. Given nondeterministic models of system and its specification, we study the design of a supervisor (possibly nondeterministic) such that the controlled system is bisimilar to the specification. We obtain a small model theorem showing that a supervisor exists if and only if it exists over a certain finite state space, namely the power set of Cartesian product of system and specification state spaces. Also, the notion of state-controllability is introduced as part of a necessary and sufficient condition for the existence of a supervisor. In the special case of deterministic systems, we provide an existence condition that can be verified linearly in both system and specification states.

In this paper, we study supervisory control of a nondeterministic systems -- probabilistic discrete event systems. As language equivalence is not an adequate notion of behavioral equivalence for some nondeterministic systems, here we use the finest known notion of equivalence: bisimulation equivalence. The design of a supervisor such that the controlled system is bisimilar to the specification is studied and a model theorem obtained, in which it shows that a supervisor exists if and only if it exists over a certain finite state space. Also, notions about state-controllability are introduced as part of a necessary and sufficient condition for the existence of the supervisor.

This paper gives a decentralized approach to the problem of failure prognosis in the framework of fuzzy discrete event systems (FDES). A notion of co-predictability is formalized for decentralized prognosis of FDESs, where several local agents with fuzzy observability rather than crisp observability are used in the prognosis task. An FDES is said to be co-predictable if each faulty event can be predicted prior to its occurrence by at least one local agent using the observability of fuzzy events. The verification of the decentralized predictability is performed by constructing a fuzzy co-verifier from a given FDES. The complexity of the fuzzy co-verifier is polynomial with respect to the FDES being predicted, and is exponential with respect to the number of the local prognosis agents. Then, a necessary and sufficient condition for the co-predictability of FDESs is given. In addition, we show that the proposed method may be used to deal with the decentralized prognosis for both FDESs and crisp DESs. Finally, to illustrate the effectiveness of the approach, some examples are provided.

본 논문은 Crisp Discrete Event System(CDES)에서 다룰 수 없는 특성을 가지는 의료진단이나 교통제어와 같이 애매하거나 불확실한 판단 그리고 관련성이 모호한 판단의 근거들에 의해 결정되어지는 사건들로 이루어진 Fuzzy Discrete Event System(FDES)의 모델링 방법과 그 응용에 대하여 연구하였다. 일반적인 CDES는 모델링 방법이 많이 연구되어져 왔으나, FDES는 발생되어지는 사건들의 정성적인 특성과 적용되어지는 경우가 드문 이유로 거의 연구되어져 있지 않다. 본 논문에서는 Fuzzy Timed Transition Petri Net(FTTPN)으로 FDES인 교통 시스템을 모델링하고 교통 신호제어기를 설계하였다. This paper deals with modeling method and application of Fuzzy Discrete Event System(FDES). FDES have characteristics which Crisp Discrete Event System(CDES) can't deals with and is constituted with the events that is determined by vague and uncertain judgement like biomedical or traffic control. In general, the modeling method of CDES has been studied many times, but that of FDES hasn't been nearly studied by qualitative character and scarcity of applicated system. This paper models traffic system with FDES's character in FTTPN and designs a traffic signal controller.

This paper presents a novel diagnosis approach for crisis management using fuzzy discrete event system (model). The method exploits the output events and membership value of each active state as input events of the diagnoser (diagnosis module). In our work the choice of fuzzy system representation is justified by the assumption that, during crisis management, the stress and/or impact emotion of the teams involved in crisis management must be taken into account and the evolution of the situation may not necessarily in one active state. The membership value generated by the model can be used for the possible control action during the crisis management.

The decentralized supervisory control problem of discrete event systems with local specifications is studied. A necessary and sufficient condition is obtained for the existence of modular supervisors for ensuring that a group of local specifications is achieved by the controlled system. For illustration an example of a simple manufacturing system is given. The paper provides a modular approach for the design of supervisors for large systems.

This paper presents a novel computational model of robotic visual attention using fuzzy discrete event system (FDES). The method attempts to implement the Biased competitive hypothesis, where the bottom-up bias (or object saliency) is combined with the top-down preference (or specific object bias) for attention modeling. In the proposed implementation of biased competitive hypothesis, FDES is used to model the sensory feedback from the environment to generate the object-saliency. An arbiter combines the top-down bias with the object-saliency and selects an appropriate object for visual attention. The FDES-based architecture provides the opportunity to implement heuristic-based reasoning using the state-transition structure. It also employs fuzzy logic to incorporate deterministic vagueness of human reasoning. The state-based generation of the object saliency prevents abrupt change in visual attention, which helps generating consistent motion commands for the camera. This method uses FDES-based observability and controllability to measure the decision vagueness and sudden change in the visual attention. These measurements are used to modulate the pantile commands of the camera to produces slower speed when the attention is suddenly distracted. Experimental results are also presented to validate different aspects of the proposed system.

This paper aims to investigate safe diagnosis of fuzzy discrete-event systems (FDESs) under the decentralized framework. The notion of safe codiagnosability of FDESs is formalized to capture the property of systems that each occurrence of failures can be detected by at least one local diagnoser with a certain degree before any unsafe forbidden operation is executed. After introducing a fuzzy automaton called the recognizer to distinguish the forbidden strings from the illegal language, a safe codiagnoser is constructed to perform decentralized safe diagnosis of FDESs. In particular, a necessary and sufficient condition of safe codiagnosability of FDESs is derived, which extends the existing main results of safe diagnosability of FDESs from the centralized setting to the decentralized case.

Air conditioning (AC) system is a nonlinear, asynchronous and uncertain natured system. In this paper a fuzzy discrete event systems (FDES) is introduced in the research of air conditioning control. A fuzzy automaton for air conditioning system is given. A modeling method is proposed and a control model has been set up for the air conditioning system. Cost optimization is based on set up priorities in events combination and effectiveness function optimization is based on forward-looking tree. The simulation results show that the optimal control can be better resolved with FDES in air conditioning system. Practically application of this method is observed reduce in energy consumption of the system.

Fuzzy discrete event systems (FDESs) have been introduced in recent years to model systems whose discrete states or discrete state transitions can be uncertain and are, hence, determined by a possibility degree. This paper develops an FDES framework for the control of sampled data systems that have to fulfill multiple objectives. The choice of a fuzzy system representation is justified by the assumption of a controller realization that depends on various potentially imprecise sensor measurements. The proposed framework consists of three basic steps that are performed at each sampling instant. First, the current fuzzy state of the system is determined by a sensor evaluation. Second, the fuzzy state in the future sampling instant is predicted for all possible control actions of the system. Finally, an original multiobjective weighting strategy is proposed to determine the control action to be applied in the current sampling instant. The features of the proposed approach are demonstrated by a detailed mobile robot example, which includes a simulation study.