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

An integrated approach to global synchronization and state estimation for nonlinear singularly perturbed complex networks

This paper aims to establish a unified framework to handle both the exponential synchronization and state estimation problems for a class of nonlinear singularly perturbed complex networks (SPCNs). Each node in the SPCN comprises both 'slow' and 'fast' dynamics that reflects the singular perturbation behavior. General sector-like nonlinear function is employed to describe the nonlinearities existing in the network. All nodes in the SPCN have the same structures and properties. By utilizing a novel Lyapunov functional and the Kronecker product, it is shown that the addressed SPCN is synchronized if certain matrix inequalities are feasible. The state estimation problem is then studied for the same complex network, where the purpose is to design a state estimator to estimate the network states through available output measurements such that dynamics (both slow and fast) of the estimation error is guaranteed to be globally asymptotically stable. Again, a matrix inequality approach is developed for the state estimation problem. Two numerical examples are presented to verify the effectiveness and merits of the proposed synchronization scheme and state estimation formulation. It is worth mentioning that our main results are still valid even if the slow subsystems within the network are unstable

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

Distributed Decision Through Self-Synchronizing Sensor Networks in the Presence of Propagation Delays and Asymmetric Channels

In this paper we propose and analyze a distributed algorithm for achieving globally optimal decisions, either estimation or detection, through a self-synchronization mechanism among linearly coupled integrators initialized with local measurements. We model the interaction among the nodes as a directed graph with weights (possibly) dependent on the radio channels and we pose special attention to the effect of the propagation delay occurring in the exchange of data among sensors, as a function of the network geometry. We derive necessary and sufficient conditions for the proposed system to reach a consensus on globally optimal decision statistics. One of the major results proved in this work is that a consensus is reached with exponential convergence speed for any bounded delay condition if and only if the directed graph is quasi-strongly connected. We provide a closed form expression for the global consensus, showing that the effect of delays is, in general, the introduction of a bias in the final decision. Finally, we exploit our closed form expression to devise a double-step consensus mechanism able to provide an unbiased estimate with minimum extra complexity, without the need to know or estimate the channel parameters.Comment: To be published on IEEE Transactions on Signal Processin

Effective synchronization of a class of Chua's chaotic systems using an exponential feedback coupling

In this work a robust exponential function based controller is designed to synchronize effectively a given class of Chua's chaotic systems. The stability of the drive-response systems framework is proved through the Lyapunov stability theory. Computer simulations are given to illustrate and verify the method.Comment: 12 pages, 18 figure

A continuous-time analysis of distributed stochastic gradient

We analyze the effect of synchronization on distributed stochastic gradient algorithms. By exploiting an analogy with dynamical models of biological quorum sensing -- where synchronization between agents is induced through communication with a common signal -- we quantify how synchronization can significantly reduce the magnitude of the noise felt by the individual distributed agents and by their spatial mean. This noise reduction is in turn associated with a reduction in the smoothing of the loss function imposed by the stochastic gradient approximation. Through simulations on model non-convex objectives, we demonstrate that coupling can stabilize higher noise levels and improve convergence. We provide a convergence analysis for strongly convex functions by deriving a bound on the expected deviation of the spatial mean of the agents from the global minimizer for an algorithm based on quorum sensing, the same algorithm with momentum, and the Elastic Averaging SGD (EASGD) algorithm. We discuss extensions to new algorithms which allow each agent to broadcast its current measure of success and shape the collective computation accordingly. We supplement our theoretical analysis with numerical experiments on convolutional neural networks trained on the CIFAR-10 dataset, where we note a surprising regularizing property of EASGD even when applied to the non-distributed case. This observation suggests alternative second-order in-time algorithms for non-distributed optimization that are competitive with momentum methods.Comment: 9/14/19 : Final version, accepted for publication in Neural Computation. 4/7/19 : Significant edits: addition of simulations, deep network results, and revisions throughout. 12/28/18: Initial submissio

Optimal Distributed Controller Design for Nonlinear Coupled Dynamical Networks

This paper is concerned with the optimal distributed impulsive controller design for globally exponential synchronization of nonlinear dynamical networks with coupling delay. By the Lyapunov-Razumikhin method, a novel criterion is proposed to guarantee the global exponential synchronization of the coupled delayed network with distributed impulsive control in terms of matrix inequalities. The sum of coupling strengths of the distributed impulsive control is minimized to save the control effort. Finally, the effectiveness of the proposed method has been demonstrated by some simulations

Time-and event-driven communication process for networked control systems: A survey

Copyright © 2014 Lei Zou 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 recent years, theoretical and practical research topics on networked control systems (NCSs) have gained an increasing interest from many researchers in a variety of disciplines owing to the extensive applications of NCSs in practice. In particular, an urgent need has arisen to understand the effects of communication processes on system performances. Sampling and protocol are two fundamental aspects of a communication process which have attracted a great deal of research attention. Most research focus has been on the analysis and control of dynamical behaviors under certain sampling procedures and communication protocols. In this paper, we aim to survey some recent advances on the analysis and synthesis issues of NCSs with different sampling procedures (time-and event-driven sampling) and protocols (static and dynamic protocols). First, these sampling procedures and protocols are introduced in detail according to their engineering backgrounds as well as dynamic natures. Then, the developments of the stabilization, control, and filtering problems are systematically reviewed and discussed in great detail. Finally, we conclude the paper by outlining future research challenges for analysis and synthesis problems of NCSs with different communication processes.This work was supported in part by the National Natural Science Foundation of China under Grants 61329301, 61374127, and 61374010, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany