Dissipativity analysis for discrete time-delay fuzzy neural networks with Markovian jumps

This paper is concerned with the dissipativity analysis and design of discrete Markovian jumping neural networks with sector-bounded nonlinear activation functions and time-varying delays represented by Takagi–Sugeno fuzzy model. The augmented fuzzy neural networks with Markovian jumps are first constructed based on estimator of Luenberger observer type. Then, applying piecewise Lyapunov–Krasovskii functional approach and stochastic analysis technique, a sufficient condition is provided to guarantee that the augmented fuzzy jump neural networks are stochastically dissipative. Moreover, a less conservative criterion is established to solve the dissipative state estimation problem by using matrix decomposition approach. Furthermore, to reduce the computational complexity of the algorithm, a dissipative estimator is designed to ensure stochastic dissipativity of the error fuzzy jump neural networks. As a special case, we have also considered the mixed H∞ and passive analysis of fuzzy jump neural networks. All criteria can be formulated in terms of linear matrix inequalities. Finally, two examples are given to show the effectiveness and potential of the new design techniques.Yingqi Zhang, Peng Shi, Ramesh K. Agarwal, and Yan Sh

Nonlinear analysis of dynamical complex networks

Copyright © 2013 Zidong Wang 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.Complex networks are composed of a large number of highly interconnected dynamical units and therefore exhibit very complicated dynamics. Examples of such complex networks include the Internet, that is, a network of routers or domains, the World Wide Web (WWW), that is, a network of websites, the brain, that is, a network of neurons, and an organization, that is, a network of people. Since the introduction of the small-world network principle, a great deal of research has been focused on the dependence of the asymptotic behavior of interconnected oscillatory agents on the structural properties of complex networks. It has been found out that the general structure of the interaction network may play a crucial role in the emergence of synchronization phenomena in various fields such as physics, technology, and the life sciences

Dissipative Analysis and Synthesis of Control for TS Fuzzy Markovian Jump Neutral Systems

This paper is focused on stochastic stability and strictly dissipative control design for a class of Takagi-Sugeno (TS) fuzzy neutral time delayed control systems with Markovian jumps. The main aim of this paper is to design a strictly dissipative controller such that the closed-loop TS fuzzy control system is stochastically stable, and also the disturbance rejection attenuation is obtained to a given level by means of the H∞ performance index. Intensive analysis is carried out to obtain sufficient conditions for the existence of desired dissipative controller which ensures both the stochastic stability and the strictly dissipative performance. The main advantage of the proposed technique is that it is possible to obtain the dissipative controller with less control effort and also, as special cases, robust H∞ control with the prescribed H∞ performance under given constraints and passivity control can be obtained for the considered systems. Also, the existence condition of the fuzzy dissipative controller can be obtained in terms of linear matrix inequalities. Finally, a practical example based on truck-trailer model is provided to demonstrate the effectiveness and feasibility of the proposed design technique

Quantized passive filtering for switched delayed neural networks

The issue of quantized passive filtering for switched delayed neural networks with noise interference is studied in this paper. Both arbitrary and semi-Markov switching rules are taken into account. By choosing Lyapunov functionals and applying several inequality techniques, sufficient conditions are proposed to ensure the filter error system to be not only exponentially stable, but also exponentially passive from the noise interference to the output error. The gain matrix for the proposed quantized passive filter is able to be determined through the feasible solution of linear matrix inequalities, which are computationally tractable with the help of some popular convex optimization tools. Finally, two numerical examples are given to illustrate the usefulness of the quantized passive filter design methods

A novel nonzero functional method to extended dissipativity analysis for neural networks with Markovian jumps

This paper explored the topic of extended dissipativity analysis for Markovian jump neural networks (MJNNs) that were influenced by time-varying delays. A distinctive Lyapunov functional, distinguished by a non-zero delay-product types, was presented. This was achieved by combining a Wirtinger-based double integral inequality with a flexible matrix set. This novel methodology addressed the limitations of the slack matrices found in earlier research. As a result, a fresh condition for extended dissipativity in MJNNs was formulated, utilizing an exponential type reciprocally convex inequality in conjunction with the newly introduced nonzero delay-product types. A numerical example was included to demonstrate the effectiveness of the proposed methodology

Nonfragile H

This paper is concerned with the nonfragile H∞ control problem for stochastic systems with Markovian jumping parameters and random packet losses. The communication between the physical plant and controller is assumed to be imperfect, where random packet losses phenomenon occurs in a random way. Such a phenomenon is represented by a stochastic variable satisfying the Bernoulli distribution. The purpose is to design a nonfragile controller such that the resulting closed-loop system is stochastically mean square stable with a guaranteed H∞ performance level γ. By using the Lyapunov function approach, some sufficient conditions for the solvability of the previous problem are proposed in terms of linear matrix inequalities (LMIs), and a corresponding explicit parametrization of the desired controller is given. Finally, an example illustrating the effectiveness of the proposed approach is presented

Protocol-based state estimation for delayed Markovian jumping neural networks

National Natural Science Foundation of China; the PetroChina Innovation Foundation; the China Postdoctoral Science Foundation; the Natural Science Foundation of Heilongjiang Province of China; the Northeast Petroleum University Innovation Foundation For Postgraduate; the Alexander von Humboldt Foundation of German

UNFIS: A Novel Neuro-Fuzzy Inference System with Unstructured Fuzzy Rules for Classification

An important constraint of Fuzzy Inference Systems (FIS) is their structured rules defined based on evaluating all input variables. Indeed, the length of all fuzzy rules and the number of input variables are equal. However, in many decision-making problems evaluating some conditions on a limited set of input variables is sufficient to decide properly (unstructured rules). Therefore, this constraint limits the performance, generalization, and interpretability of the FIS. To address this issue, this paper presents a neuro-fuzzy inference system for classification applications that can select different sets of input variables for constructing each fuzzy rule. To realize this capability, a new fuzzy selector neuron with an adaptive parameter is proposed that can select input variables in the antecedent part of each fuzzy rule. Moreover, in this paper, the consequent part of the Takagi-Sugeno-Kang FIS is also changed properly to consider only the selected set of input variables. To learn the parameters of the proposed architecture, a trust-region-based learning method (General quasi-Levenberg-Marquardt (GqLM)) is proposed to minimize cross-entropy in multiclass problems. The performance of the proposed method is compared with some related previous approaches in some real-world classification problems. Based on these comparisons the proposed method has better or very close performance with a parsimonious structure consisting of unstructured fuzzy