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

Designing power system stabilizer for multimachine power system using neuro-fuzzy algorithm

This paper describes a design procedure for a fuzzy logic based power system stabilizer (FLPSS) and adaptive neuro-fuzzy inference system (ANFIS) and investigates their robustness for a multi-machine power system. Speed deviation of a machine and its derivative are chosen as the input signals to the FLPSS. A four-machine and a two-area power system is used as the case study. Computer simulations for the test system subjected to transient disturbances i.e. a three phase fault, were carried out and the results showed that the proposed controller is able to prove its effectiveness and improve the system damping when compared to a conventional lead-lag based power system stabilizer controller

Evidential relational clustering using medoids

In real clustering applications, proximity data, in which only pairwise similarities or dissimilarities are known, is more general than object data, in which each pattern is described explicitly by a list of attributes. Medoid-based clustering algorithms, which assume the prototypes of classes are objects, are of great value for partitioning relational data sets. In this paper a new prototype-based clustering method, named Evidential C-Medoids (ECMdd), which is an extension of Fuzzy C-Medoids (FCMdd) on the theoretical framework of belief functions is proposed. In ECMdd, medoids are utilized as the prototypes to represent the detected classes, including specific classes and imprecise classes. Specific classes are for the data which are distinctly far from the prototypes of other classes, while imprecise classes accept the objects that may be close to the prototypes of more than one class. This soft decision mechanism could make the clustering results more cautious and reduce the misclassification rates. Experiments in synthetic and real data sets are used to illustrate the performance of ECMdd. The results show that ECMdd could capture well the uncertainty in the internal data structure. Moreover, it is more robust to the initializations compared with FCMdd.Comment: in The 18th International Conference on Information Fusion, July 2015, Washington, DC, USA , Jul 2015, Washington, United State

Fuzzy sphere bimodule, ABS construction to the exact soliton solutions

In this paper, we set up the bi-module of the algebra ${\cal A}$ on fuzzy sphere. Based on the differential operators in moving frame, we generalize the ABS construction into fuzzy sphere case. The applications of ABS construction are investigated in various physical systems.Comment: Latex file without figure, 13 page

Critical Behaviour of the Fuzzy Sphere

We study a multi-matrix model whose low temperature phase is a fuzzy sphere that undergoes an evaporation transition as the temperature is increased. We investigate finite size scaling of the system as the limiting temperature of stability of the fuzzy sphere phase is approached. We find on theoretical grounds that the system should obey scaling with specific heat exponent \alpha=1/2, shift exponent \bar \lambda=4/3 and that the peak in the specific heat grows with exponent \bar \omega=2/3. Using hybrid Monte Carlo simulations we find good collapse of specific heat data consistent with a scaling ansatz which give our best estimates for the scaling exponents as \alpha=0.50 \pm 0.01,\bar \lambda=1.41 \pm 0.08 and \bar \omega=0.66 \pm 0.08 .Comment: 30 pages, 10 figure

Fuzzy stability analysis of regenerative chatter in milling

During machining, unstable self-excited vibrations known as regenerative chatter can occur, causing excessive tool wear or failure, and a poor surface finish on the machined workpiece. Consequently it is desirable to predict, and hence avoid the onset of this instability. Regenerative chatter is a function of empirical cutting coefficients, and the structural dynamics of the machine-tool system. There can be significant uncertainties in the underlying parameters, so the predicted stability limits do not necessarily agree with those found in practice. In the present study, fuzzy arithmetic techniques are applied to the chatter stability problem. It is first shown that techniques based upon interval arithmetic are not suitable for this problem due to the issue of recursiveness. An implementation of fuzzy arithmetic is then developed based upon the work of Hanss and Klimke. The arithmetic is then applied to two techniques for predicting milling chatter stability: the classical approach of Altintas, and the time-finite element method of Mann. It is shown that for some cases careful programming can reduce the computational effort to acceptable levels. The problem of milling chatter uncertainty is then considered within the framework of Ben-Haim's information-gap theory. It is shown that the presented approach can be used to solve process design problems with robustness to the uncertain parameters. The fuzzy stability bounds are then compared to previously published data, to investigate how uncertainty propagation techniques can offer more insight into the accuracy of chatter predictions