连续计时离散事件系统监控及其可观性

本文提出了一种带有连续时间变量的离散事件系统(称为计时离散事件系统)结构模型.通过讨论计时语言的性质,如封闭性、可控性以及可观性,研究了计时离散事件系统的监控综合问题,并基于这些性质,分别提出了计时离散事件系统在完全可观与部分可观条件下监控器存在的充要条件.     

分布式模糊离散事件系统的故障预测

本文研究分布式模糊离散事件系统的故障预测问题.先根据系统的模糊特性,提出一种分布式模糊离散事件系统的协同可预测性的形式化方法,使分布式模糊离散事件系统的协同可预测度不小于各分站点的局部可预测度.通过构造协同预测验证器,提出一种基于协同预测验证器的协同预测算法,并得到一个关于分布式模糊离散事件系统协同可预测性的充分必要条件.     

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 modeled 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.     

The relationship of controllability between classical and fuzzy discrete-event systems

We have known that the controllability of classical discrete-event systems has already been extended into fuzzy discrete-event systems. In this paper, firstly, we recall some related definitions and results of the controllability for classical and fuzzy discrete-event systems, respectively. Secondly, we are concerned with the relationship of the controllability between classical and fuzzy discrete-event systems. In particular, we show that there is an equivalence of the controllability between the two systems to some extent, some special proofs are also presented. Finally, we use this equivalence to extend some general controllability properties of classical discrete-event systems into fuzzy ones.     

From a Gaussian mixture model to additive fuzzy systems

This work explores how a kind of probabilistic system, namely the Gaussian mixture model (GMM), can be translated to an additive fuzzy system. We will prove the mathematical equivalence between the conditional mean of a GMM, and the defuzzified output of a generalized fuzzy model (GFM). The relationship between a GMM and a GFM, and the conditions for GMM to GFM translation will be made explicit in the form of theorems. The work will then extend to special cases of the GFM, specifically the Mamdani-Larsen and Takagi-Sugeno fuzzy models. The possibility of reverse translation, that is, from a GFM to a GMM will also be discussed. Finally, we will consider the generality of a GMM, specifically how it can approximate other distribution functions.     

From classic CNC systems to cloud-based technology and back

The transition to cloud-based technology in the field of CNC systems requires significant changes to the architecture of the control system, which is associated with a partial loss of funds already invested in its development. The paper suggests an approach to the architectural organization of the CNC system modules, which allows reconfiguring the control system on-the-fly in order to form any of the possible solutions: the classical layout of the CNC system, the extended layout (using an external interpolator), or the cloud layout of the CNC system. Experimental studies were carried using the 3-axis machining of parts on a milling machine with the cloud layout of the CNC system.     

Robustness of supervisors for discrete-event systems

Supervisory control in the context of ω-languages is considered. The nominal supervisor design problem is to find a non-blocking supervisor for a nominal plant such that the closed-loop infinite behavior equals a specified closed-loop behavior. The robustness of solutions to the nominal problem is defined with respect to variations in the plant. It is shown there exists a supervisor solving the nominal problem which maximizes the set of plants for which the closed-loop languages for all other plants in the set satisfy lower and upper bounds in the sense of language containment. Computational issues are discussed and the theoretical results are illustrated with an example     

State observability and condition observability for a class of interacting discrete event systems

This paper introduces the concepts of state observability and condition observability for condition systems, a class of systems composed of discrete state components which interact via discrete binary signals called conditions. Given a set of externally observed conditions, state observability implies that the state of the system can be determined from the observations, and condition observability implies that all unobserved input and output conditions of the system can be determined from the observations. In this paper, we present a class of systems which is state observable and condition observable. We present a method to synthesize an observer system to provide state and condition signal estimates for a single component subsystem.     

Pade approximation for stochastic discrete-event systems

We show that Pade approximation can be effectively used for approximation of performance functions in discrete-event systems. The method is (1) obtaining the MacLaurin coefficients of the performance function and (2) finding a Pade approximant from the MacLaurin coefficients and use it to approximate the function. We use the method with the expected number of renewals in a random interval, GI/G/1 systems, and inventory systems. The results are very good     

Reduced supervisors for timed discrete-event systems

The design of reduced supervisors, suboptimal but easier to compute, is placed in a general perspective. From this vantage point, we consider a timed discrete-event system, and compute a reduced supervisor based on an abstraction of the plant model in which time is measured with a slower clock. Such a model is simpler than the original, but has richer untimed behavior. Thus, a time-independent specification met by the closed-loop reduced system is also met by the original system when controlled by the same supervisor. The idea is illustrated with a simple example.     

Uniformization based sensitivity estimation for a class of discrete-event systems

Infinitestimal Perturbation Analysis (IPA) estimators are based on particular couplings of parameteric families of discrete event systems where small changes in the parameter value, typically, cause small changes in the timing of events and, for finite horizons, the sequence of states visisted remains the same. We consider another coupling approach based on the uniformization procedure and a simple generalization of it. In our case any small change in the parameter value causes a change in the state of the system; our parameterization of trajectories keeps them highly synchronized, hence the effect of such changes can be estimated, sometimes efficiently. In this framework, we define three tupes of performance sensitivity estimators for a broad class of performance measures and with respect to a range of parameter values. Performance measures on finite deterministic horizons are considered and it is shown that they are unbiased under mild conditions. We show that for some systems the derivative estimators can be calculated from a nominal sample path of the system.     

Discrete-time observability for distributed parameter systems

The aim of this paper is to study the observability for systems described by first-order evolution equations and for those described by second-order evolution equations in the case of discrete-time observations. For the systems with a finite number of sensors we present necessary and sufficient conditions for observability. We show that these distributed parameter systems are never finite-step observable. We give the restricted sets of the initial-state spaces whose elements are N-step observable. We also investigate the relations between the systems with discrete-time observations and the systems with continuous-time observations from the viewpoint of observability Moreover, we see the essential difference between the parabolic case and the hyperbolic case.     

Diagnosis of a class of distributed discrete-event systems

Discrete-event modeling can be applied to a large variety of physical systems, in order to support different tasks, including fault detection, monitoring, and diagnosis. The paper focuses on the model-based diagnosis of a class of distributed discrete-event systems, called active systems. An active system, which is designed to react to possibly harmful external events, is modeled as a network of communicating automata, where each automaton describes the behavior of a system component. Unlike other approaches based on the synchronous composition of automata and on the off-line creation of the model of the entire system, the proposed diagnostic technique deals with asynchronous events and does not need any global diagnoser to be built. Instead, the current approach features a problem-decomposition/solution-composition nature whose core is the online progressive reconstruction of the behavior of the active system, guided by the available observations. This incremental technique makes effective the diagnosis of large-scale active systems, for which the one-shot generation of the global model is almost invariably impossible in practice. The diagnostic method encompasses three steps: (1) reconstruction planning; (2) behavior reconstruction; and (3) diagnosis generation. Step 1 draws a hierarchical decomposition of the behavior reconstruction problem. Reconstruction is made in Step 2, where an intensional representation of all the dynamic behaviors which are consistent with the available system observation is produced. Diagnosis is eventually generated in Step 3, based on the faulty evolutions incorporated within the reconstructed behaviors. The modular approach is formally defined, with special emphasis on Steps 2 and 3, and applied to the power transmission network domain     

Sufficiency for diagnosability of stochastic discrete-event systems and a polynomial-time verification

The notion of diagnosability of stochastic discrete-event systems (SDESs) was introduced in the literature, but the method for verifying the diagnosability of SDESs was exponential. However, is there a sufficient condition of diagnosability of SDESs that can be tested with polynomial method? In this paper, we present a sufficient condition of diagnosability of SDESs based on a constructive testing automaton, and a polynomial method is proposed to test the condition.     

Safe diagnosability for fault-tolerant supervision of discrete-event systems

The problem of achieving fault-tolerant supervision of discrete-event systems is considered from the viewpoint of safe and timely diagnosis of unobservable faults. To this end, the new property of safe diagnosability is introduced and studied. Standard definitions of diagnosability of discrete-event systems deal with the problem of detecting the occurrence of unobservable fault events using model-based inferencing from observed sequences of events. In safe diagnosability, it is required in addition that fault detection occur prior to the execution of a given set of forbidden strings in the failed mode of operation of the system. For instance, this constraint could be required to prevent local faults from developing into failures that could cause safety hazards. If the system is safe diagnosable, reconfiguration actions could be forced upon the detection of faults prior to the execution of unsafe behaviour, thus achieving the objective of fault-tolerant supervision. Necessary and sufficient conditions for safe diagnosability are derived. In addition, the problem of explicitly considering safe diagnosability in controller design, termed “active safe diagnosis problem”, is formulated and solved. A brief discussion of safe diagnosability for timed models of discrete-event systems is also provided.     

Robust observability for a class of time-varying discrete-time uncertain systems

This paper introduces a concept of robust observability for a class of uncertain discrete-time systems. This notion is an extension of the standard notion of observability for discrete-time, linear time-varying systems. The uncertainty and noise are modelled deterministically via a sum quadratic constraint. A necessary and sufficient condition for robust observability is presented in terms of existence of a suitable solution to a Riccati difference equation. The set of possible initial states given noisy measurements over a finite number of sampling periods is shown to be an ellipsoid.