State estimation for discrete-time neural networks with Markov-mode-dependent lower and upper bounds on the distributed delays

Copyright @ 2012 Springer VerlagThis paper is concerned with the state estimation problem for a new class of discrete-time neural networks with Markovian jumping parameters and mixed time-delays. The parameters of the neural networks under consideration switch over time subject to a Markov chain. The networks involve both the discrete-time-varying delay and the mode-dependent distributed time-delay characterized by the upper and lower boundaries dependent on the Markov chain. By constructing novel Lyapunov-Krasovskii functionals, sufficient conditions are firstly established to guarantee the exponential stability in mean square for the addressed discrete-time neural networks with Markovian jumping parameters and mixed time-delays. Then, the state estimation problem is coped with for the same neural network where the goal is to design a desired state estimator such that the estimation error approaches zero exponentially in mean square. The derived conditions for both the stability and the existence of desired estimators are expressed in the form of matrix inequalities that can be solved by the semi-definite programme method. A numerical simulation example is exploited to demonstrate the usefulness of the main results obtained.This work was supported in part by the Royal Society of the U.K., the National Natural Science Foundation of China under Grants 60774073 and 61074129, and the Natural Science Foundation of Jiangsu Province of China under Grant BK2010313

A review on analysis and synthesis of nonlinear stochastic systems with randomly occurring incomplete information

Copyright q 2012 Hongli Dong 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.In the context of systems and control, incomplete information refers to a dynamical system in which knowledge about the system states is limited due to the difficulties in modeling complexity in a quantitative way. The well-known types of incomplete information include parameter uncertainties and norm-bounded nonlinearities. Recently, in response to the development of network technologies, the phenomenon of randomly occurring incomplete information has become more and more prevalent. Such a phenomenon typically appears in a networked environment. Examples include, but are not limited to, randomly occurring uncertainties, randomly occurring nonlinearities, randomly occurring saturation, randomly missing measurements and randomly occurring quantization. Randomly occurring incomplete information, if not properly handled, would seriously deteriorate the performance of a control system. In this paper, we aim to survey some recent advances on the analysis and synthesis problems for nonlinear stochastic systems with randomly occurring incomplete information. The developments of the filtering, control and fault detection problems are systematically reviewed. Latest results on analysis and synthesis of nonlinear stochastic systems are discussed in great detail. In addition, various distributed filtering technologies over sensor networks are highlighted. Finally, some concluding remarks are given and some possible future research directions are pointed out. © 2012 Hongli Dong et al.This work was supported in part by the National Natural Science Foundation of China under Grants 61273156, 61134009, 61273201, 61021002, and 61004067, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National Science Foundation of the USA under Grant No. HRD-1137732, and the Alexander von Humboldt Foundation of German

Synchronization of coupled neutral-type neural networks with jumping-mode-dependent discrete and unbounded distributed delays

This is the post-print version of the Article. The official published version can be accessed from the links below - Copyright @ 2013 IEEE.In this paper, the synchronization problem is studied for an array of N identical delayed neutral-type neural networks with Markovian jumping parameters. The coupled networks involve both the mode-dependent discrete-time delays and the mode-dependent unbounded distributed time delays. All the network parameters including the coupling matrix are also dependent on the Markovian jumping mode. By introducing novel Lyapunov-Krasovskii functionals and using some analytical techniques, sufficient conditions are derived to guarantee that the coupled networks are asymptotically synchronized in mean square. The derived sufficient conditions are closely related with the discrete-time delays, the distributed time delays, the mode transition probability, and the coupling structure of the networks. The obtained criteria are given in terms of matrix inequalities that can be efficiently solved by employing the semidefinite program method. Numerical simulations are presented to further demonstrate the effectiveness of the proposed approach.This work was supported in part by the Royal Society of the U.K., the National Natural Science Foundation of China under Grants 61074129, 61174136 and 61134009, and the Natural Science Foundation of Jiangsu Province of China under Grants BK2010313 and BK2011598

Exponential synchronization of complex networks with Markovian jump and mixed delays

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2008 Elsevier LtdIn this Letter, we investigate the exponential synchronization problem for an array of N linearly coupled complex networks with Markovian jump and mixed time-delays. The complex network consists of m modes and the network switches from one mode to another according to a Markovian chain with known transition probability. The mixed time-delays are composed of discrete and distributed delays, both of which are mode-dependent. The nonlinearities imbedded with the complex networks are assumed to satisfy the sector condition that is more general than the commonly used Lipschitz condition. By making use of the Kronecker product and the stochastic analysis tool, we propose a novel Lyapunov–Krasovskii functional suitable for handling distributed delays and then show that the addressed synchronization problem is solvable if a set of linear matrix inequalities (LMIs) are feasible. Therefore, a unified LMI approach is developed to establish sufficient conditions for the coupled complex network to be globally exponentially synchronized in the mean square. Note that the LMIs can be easily solved by using the Matlab LMI toolbox and no tuning of parameters is required. A simulation example is provided to demonstrate the usefulness of the main results obtained.This work was supported in part by the Biotechnology and Biological Sciences Research Council (BBSRC) of the UK under Grants BB/C506264/1 and 100/EGM17735, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grants GR/S27658/01 and EP/C524586/1, an International Joint Project sponsored by the Royal Society of the UK, the Natural Science Foundation of Jiangsu Province of China under Grant BK2007075, the National Natural Science Foundation of China under Grant 60774073, and the Alexander von Humboldt Foundation of Germany

Robust H∞ filtering for a class of nonlinear networked systems with multiple stochastic communication delays and packet dropouts

Copyright [2010] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, the robust H∞ filtering problem is studied for a class of uncertain nonlinear networked systems with both multiple stochastic time-varying communication delays and multiple packet dropouts. A sequence of random variables, all of which are mutually independent but obey Bernoulli distribution, are introduced to account for the randomly occurred communication delays. The packet dropout phenomenon occurs in a random way and the occurrence probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution in the interval. The discrete-time system under consideration is also subject to parameter uncertainties, state-dependent stochastic disturbances and sector-bounded nonlinearities. We aim to design a linear full-order filter such that the estimation error converges to zero exponentially in the mean square while the disturbance rejection attenuation is constrained to a give level by means of the H∞ performance index. Intensive stochastic analysis is carried out to obtain sufficient conditions for ensuring the exponential stability as well as prescribed H∞ performance for the overall filtering error dynamics, in the presence of random delays, random dropouts, nonlinearities, and the parameter uncertainties. These conditions are characterized in terms of the feasibility of a set of linear matrix inequalities (LMIs), and then the explicit expression is given for the desired filter parameters. Simulation results are employed to demonstrate the effectiveness of the proposed filter design technique in this paper.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., the Alexander von Humboldt Foundation of Germany, National Natural Science Foundation of China under Grant 60825303, 60834003, 973 Project under Grant 2009CB320600, Fok Ying Tung Education Foundation under Grant 111064, and the Youth Science Fund of Heilongjiang Province under Grant QC2009C63

Recent advances on filtering and control for nonlinear stochastic complex systems with incomplete information: A survey

This Article is provided by the Brunel Open Access Publishing Fund - Copyright @ 2012 Hindawi PublishingSome recent advances on the filtering and control problems for nonlinear stochastic complex systems with incomplete information are surveyed. The incomplete information under consideration mainly includes missing measurements, randomly varying sensor delays, signal quantization, sensor saturations, and signal sampling. With such incomplete information, the developments on various filtering and control issues are reviewed in great detail. In particular, the addressed nonlinear stochastic complex systems are so comprehensive that they include conventional nonlinear stochastic systems, different kinds of complex networks, and a large class of sensor networks. The corresponding filtering and control technologies for such nonlinear stochastic complex systems are then discussed. Subsequently, some latest results on the filtering and control problems for the complex systems with incomplete information are given. Finally, conclusions are drawn and several possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grant nos. 61134009, 61104125, 61028008, 61174136, 60974030, and 61074129, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council EPSRC of the UK under Grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

On the validity of memristor modeling in the neural network literature

An analysis of the literature shows that there are two types of non-memristive models that have been widely used in the modeling of so-called "memristive" neural networks. Here, we demonstrate that such models have nothing in common with the concept of memristive elements: they describe either non-linear resistors or certain bi-state systems, which all are devices without memory. Therefore, the results presented in a significant number of publications are at least questionable, if not completely irrelevant to the actual field of memristive neural networks

Finite-time synchronization of Markovian neural networks with proportional delays and discontinuous activations

In this paper, finite-time synchronization of neural networks (NNs) with discontinuous activation functions (DAFs), Markovian switching, and proportional delays is studied in the framework of Filippov solution. Since proportional delay is unbounded and different from infinite-time distributed delay and classical finite-time analytical techniques are not applicable anymore, new 1-norm analytical techniques are developed. Controllers with and without the sign function are designed to overcome the effects of the uncertainties induced by Filippov solutions and further synchronize the considered NNs in a finite time. By designing new Lyapunov functionals and using M-matrix method, sufficient conditions are derived to guarantee that the considered NNs realize synchronization in a settling time without introducing any free parameters. It is shown that, though the proportional delay can be unbounded, complete synchronization can still be realized, and the settling time can be explicitly estimated. Moreover, it is discovered that controllers with sign function can reduce the control gains, while controllers without the sign function can overcome chattering phenomenon. Finally, numerical simulations are given to show the effectiveness of theoretical results

Distributed state estimation in sensor networks with randomly occurring nonlinearities subject to time delays

This is the post-print version of the Article. The official published version can be accessed from the links below - Copyright @ 2012 ACM.This article is concerned with a new distributed state estimation problem for a class of dynamical systems in sensor networks. The target plant is described by a set of differential equations disturbed by a Brownian motion and randomly occurring nonlinearities (RONs) subject to time delays. The RONs are investigated here to reflect network-induced randomly occurring regulation of the delayed states on the current ones. Through available measurement output transmitted from the sensors, a distributed state estimator is designed to estimate the states of the target system, where each sensor can communicate with the neighboring sensors according to the given topology by means of a directed graph. The state estimation is carried out in a distributed way and is therefore applicable to online application. By resorting to the Lyapunov functional combined with stochastic analysis techniques, several delay-dependent criteria are established that not only ensure the estimation error to be globally asymptotically stable in the mean square, but also guarantee the existence of the desired estimator gains that can then be explicitly expressed when certain matrix inequalities are solved. A numerical example is given to verify the designed distributed state estimators.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008, 60804028 and 61174136, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM of China, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Stability Analysis for Markovian Jump Neutral Systems with Mixed Delays and Partially Known Transition Rates

The delay-dependent stability problem is studied for Markovian jump neutral systems with partial information on transition probabilities, and the considered delays are mixed and model dependent. By constructing the new stochastic Lyapunov-Krasovskii functional, which combined the introduced free matrices with the analysis technique of matrix inequalities, a sufficient condition for the systems with fully known transition rates is firstly established. Then, making full use of the transition rate matrix, the results are obtained for the other case, and the uncertain neutral Markovian jump system with incomplete transition rates is also considered. Finally, to show the validity of the obtained results, three numerical examples are provided