State estimation for coupled uncertain stochastic networks with missing measurements and time-varying delays: The discrete-time case

Copyright [2009] 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.This paper is concerned with the problem of state estimation for a class of discrete-time coupled uncertain stochastic complex networks with missing measurements and time-varying delay. The parameter uncertainties are assumed to be norm-bounded and enter into both the network state and the network output. The stochastic Brownian motions affect not only the coupling term of the network but also the overall network dynamics. The nonlinear terms that satisfy the usual Lipschitz conditions exist in both the state and measurement equations. Through available output measurements described by a binary switching sequence that obeys a conditional probability distribution, we aim to design a state estimator to estimate the network states such that, for all admissible parameter uncertainties and time-varying delays, the dynamics of the estimation error is guaranteed to be globally exponentially stable in the mean square. By employing the Lyapunov functional method combined with the stochastic analysis approach, several delay-dependent criteria are established that ensure the existence of the desired estimator gains, and then the explicit expression of such estimator gains is characterized in terms of the solution to certain linear matrix inequalities (LMIs). Two numerical examples are exploited to illustrate the effectiveness of the proposed estimator design schemes

Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time delays

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 problem of stochastic synchronization analysis is investigated for a new array of coupled discrete-time stochastic complex networks with randomly occurred nonlinearities (RONs) and time delays. The discrete-time complex networks under consideration are subject to: (1) stochastic nonlinearities that occur according to the Bernoulli distributed white noise sequences; (2) stochastic disturbances that enter the coupling term, the delayed coupling term as well as the overall network; and (3) time delays that include both the discrete and distributed ones. Note that the newly introduced RONs and the multiple stochastic disturbances can better reflect the dynamical behaviors of coupled complex networks whose information transmission process is affected by a noisy environment (e.g., Internet-based control systems). By constructing a novel Lyapunov-like matrix functional, the idea of delay fractioning is applied to deal with the addressed synchronization analysis problem. By employing a combination of the linear matrix inequality (LMI) techniques, the free-weighting matrix method and stochastic analysis theories, several delay-dependent sufficient conditions are obtained which ensure the asymptotic synchronization in the mean square sense for the discrete-time stochastic complex networks with time delays. The criteria derived are characterized in terms of LMIs whose solution can be solved by utilizing the standard numerical software. A simulation example is presented to show the effectiveness and applicability of the proposed results

Global synchronization for delayed complex networks with randomly occurring nonlinearities and multiple stochastic disturbances

This is the post print version of the article. The official published version can be obained from the link - Copyright 2009 IOP Publishing LtdThis paper is concerned with the synchronization problem for a new class of continuous time delayed complex networks with stochastic nonlinearities (randomly occurring nonlinearities), interval time-varying delays, unbounded distributed delays as well as multiple stochastic disturbances. The stochastic nonlinearities and multiple stochastic disturbances are investigated here in order to reflect more realistic dynamical behaviors of the complex networks that are affected by the noisy environment. By utilizing a new matrix functional with the idea of partitioning the lower bound h1 of the time-varying delay, we employ the stochastic analysis techniques and the properties of the Kronecker product to establish delay-dependent synchronization criteria that ensure the globally asymptotically mean-square synchronization of the addressed stochastic delayed complex networks. The sufficient conditions obtained are in the form of linear matrix inequalities (LMIs) whose solutions can be readily solved by using the standard numerical software. A numerical example is exploited to show the applicability of the proposed results.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, an International Joint Project sponsored by the Royal Society of the UK, the National 973 Program of China under Grant 2009CB320600, the National Natural Science Foundation of China under Grant 60804028, the Specialized Research Fund for the Doctoral Program of Higher Education for New Teachers under Grant 200802861044, the Teaching and Research Fund for Excellent Young Teachers at Southeast University of China, and the Alexander von Humboldt Foundation of Germany

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

Sampled-data synchronization control of dynamical networks with stochastic sampling

Copyright @ 2012 IEEEThis technical note is concerned with the sampled-data synchronization control problem for a class of dynamical networks. The sampling period considered here is assumed to be time-varying that switches between two different values in a random way with given probability. The addressed synchronization control problem is first formulated as an exponentially mean-square stabilization problem for a new class of dynamical networks that involve both the multiple probabilistic interval delays (MPIDs) and the sector-bounded nonlinearities (SBNs). Then, a novel Lyapunov functional is constructed to obtain sufficient conditions under which the dynamical network is exponentially mean-square stable. Both Gronwall's inequality and Jenson integral inequality are utilized to substantially simplify the derivation of the main results. Subsequently, a set of sampled-data synchronization controllers is designed in terms of the solution to certain matrix inequalities that can be solved effectively by using available software. Finally, a numerical simulation example is employed to show the effectiveness of the proposed sampled-data synchronization control scheme.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National Natural Science Foundation of China under Grants 61028008, 60974030, 61134009 and 61104125, the National 973 Program of China under Grant 2009CB320600, and the Alexander von Humboldt Foundation of Germany

H-infinity state estimation for discrete-time complex networks with randomly occurring sensor saturations and randomly varying sensor delays

This is the post-print of the Article. The official published version can be accessed from the link below - Copyright @ 2012 IEEEIn this paper, the state estimation problem is investigated for a class of discrete time-delay nonlinear complex networks with randomly occurring phenomena from sensor measurements. The randomly occurring phenomena include randomly occurring sensor saturations (ROSSs) and randomly varying sensor delays (RVSDs) that result typically from networked environments. A novel sensor model is proposed to describe the ROSSs and the RVSDs within a unified framework via two sets of Bernoulli-distributed white sequences with known conditional probabilities. Rather than employing the commonly used Lipschitz-type function, a more general sector-like nonlinear function is used to describe the nonlinearities existing in the network. The purpose of the addressed problem is to design a state estimator to estimate the network states through available output measurements such that, for all probabilistic sensor saturations and sensor delays, the dynamics of the estimation error is guaranteed to be exponentially mean-square stable and the effect from the exogenous disturbances to the estimation accuracy is attenuated at a given level by means of an $H_{infty}$-norm. In terms of a novel Lyapunov–Krasovskii functional and the Kronecker product, sufficient conditions are established under which the addressed state estimation problem is recast as solving a convex optimization problem via the semidefinite programming method. A simulation example is provided to show the usefulness of the proposed state estimation conditions.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 National Natural Science Foundation of China under Grants 61028008, 61134009, 61104125 and 60974030, the Natural Science Foundation of Universities in Anhui Province of China under Grant KJ2011B030, and the Alexander von Humboldt Foundation of Germany

Bounded H∞ synchronization and state estimation for discrete time-varying stochastic complex for discrete time-varying stochastic complex networks over a finite horizon

Copyright [2011] 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, new synchronization and state estimation problems are considered for an array of coupled discrete time-varying stochastic complex networks over a finite horizon. A novel concept of bounded H∞ synchronization is proposed to handle the time-varying nature of the complex networks. Such a concept captures the transient behavior of the time-varying complex network over a finite horizon, where the degree of bounded synchronization is quantified in terms of the H∞-norm. A general sector-like nonlinear function is employed to describe the nonlinearities existing in the network. By utilizing a timevarying real-valued function and the Kronecker product, criteria are established that ensure the bounded H∞ synchronization in terms of a set of recursive linear matrix inequalities (RLMIs), where the RLMIs can be computed recursively by employing available MATLAB toolboxes. The bounded H∞ 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, over a finite horizon, the dynamics of the estimation error is guaranteed to be bounded with a given disturbance attenuation level. Again, an RLMI approach is developed for the state estimation problem. Finally, two simulation examples are exploited to show the effectiveness of the results derived in this paper.This work was supported in part by the Engineering and Physical Sciences Research Council of U.K. under Grant GR/S27658/01, the National Natural Science Foundation of China under Grant 61028008 and Grant 60974030, the National 973 Program of China under Grant 2009CB320600, the International Science and Technology Cooperation Project of China under Grant 2009DFA32050, and the Alexander von Humboldt Foundation of Germany

Synchronization in an array of linearly stochastically coupled networks with time delays

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2007 Elsevier LtdIn this paper, the complete synchronization problem is investigated in an array of linearly stochastically coupled identical networks with time delays. The stochastic coupling term, which can reflect a more realistic dynamical behavior of coupled systems in practice, is introduced to model a coupled system, and the influence from the stochastic noises on the array of coupled delayed neural networks is studied thoroughly. Based on a simple adaptive feedback control scheme and some stochastic analysis techniques, several sufficient conditions are developed to guarantee the synchronization in an array of linearly stochastically coupled neural networks with time delays. Finally, an illustrate example with numerical simulations is exploited to show the effectiveness of the theoretical results.This work was jointly supported by the National Natural Science Foundation of China under Grant 60574043, the Royal Society of the United Kingdom, the Natural Science Foundation of Jiangsu Province of China under Grant BK2006093, and International Joint Project funded by NSFC and the Royal Society of the United Kingdom

Controller design for synchronization of an array of delayed neural networks using a controllable

This is the post-print version of the Article - Copyright @ 2011 ElsevierIn this paper, a controllable probabilistic particle swarm optimization (CPPSO) algorithm is introduced based on Bernoulli stochastic variables and a competitive penalized method. The CPPSO algorithm is proposed to solve optimization problems and is then applied to design the memoryless feedback controller, which is used in the synchronization of an array of delayed neural networks (DNNs). The learning strategies occur in a random way governed by Bernoulli stochastic variables. The expectations of Bernoulli stochastic variables are automatically updated by the search environment. The proposed method not only keeps the diversity of the swarm, but also maintains the rapid convergence of the CPPSO algorithm according to the competitive penalized mechanism. In addition, the convergence rate is improved because the inertia weight of each particle is automatically computed according to the feedback of fitness value. The efficiency of the proposed CPPSO algorithm is demonstrated by comparing it with some well-known PSO algorithms on benchmark test functions with and without rotations. In the end, the proposed CPPSO algorithm is used to design the controller for the synchronization of an array of continuous-time delayed neural networks.This research was partially supported by the National Natural Science Foundation of PR China (Grant No 60874113), the Research Fund for the Doctoral Program of Higher Education (Grant No 200802550007), the Key Creative Project of Shanghai Education Community (Grant No 09ZZ66), the Key Foundation Project of Shanghai(Grant No 09JC1400700), the Engineering and Physical Sciences Research Council EPSRC of the U.K. under Grant No. GR/S27658/01, an International Joint Project sponsored by the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Global synchronization control of general delayed discrete-time networks with stochastic coupling and disturbances

Copyright [2008] 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 synchronization control problem is considered for two coupled discrete-time complex networks with time delays. The network under investigation is quite general to reflect the reality, where the state delays are allowed to be time varying with given lower and upper bounds, and the stochastic disturbances are assumed to be Brownian motions that affect not only the network coupling but also the overall networks. By utilizing the Lyapunov functional method combined with linear matrix inequality (LMI) techniques, we obtain several sufficient delay-dependent conditions that ensure the coupled networks to be globally exponentially synchronized in the mean square. A control law is designed to synchronize the addressed coupled complex networks in terms of certain LMIs that can be readily solved using the Matlab LMI toolbox. Two numerical examples are presented to show the validity of our theoretical analysis results.This work was supported by the Royal Society Sino-British Fellowship Trust Award of the U.K