Design of exponential state estimators for neural networks with mixed time delays

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Elsevier Ltd.In this Letter, the state estimation problem is dealt with for a class of recurrent neural networks (RNNs) with mixed discrete and distributed delays. The activation functions are assumed to be neither monotonic, nor differentiable, nor bounded. We aim at designing a state estimator to estimate the neuron states, through available output measurements, such that the dynamics of the estimation error is globally exponentially stable in the presence of mixed time delays. By using the Laypunov–Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions to guarantee the existence of the state estimators. We show that both the existence conditions and the explicit expression of the desired estimator can be characterized in terms of the solution to an LMI. A simulation example is exploited to show the usefulness of the derived LMI-based stability conditions.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, the Alexander von Humboldt Foundation of Germany, the Natural Science Foundation of Jiangsu Education Committee of China under Grants 05KJB110154 and BK2006064, and the National Natural Science Foundation of China under Grants 10471119 and 10671172

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

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

State Estimation for Fractional-Order Complex Dynamical Networks with Linear Fractional Parametric Uncertainty

This paper deals with state estimation problem for a class of fractional-order complex dynamical networks with parametric uncertainty. The parametric uncertainty is assumed to be of linear fractional form. Firstly, based on the properties of Kronecker product and the stability of fractional-order system, a sufficient condition is derived for robust asymptotic stability of linear fractional-order augmented system. Secondly, state estimation problem is then studied for the same fractional-order complex networks, where the purpose is to design a state estimator to estimate the network state through available output measurement, the existence conditions of designing state estimator are derived using matrix's singular value decomposition and LMI techniques. These conditions are in the form of linear matrix inequalities which can be readily solved by applying the LMI toolbox. Finally, two numerical examples are provided to demonstrate the validity of our approach

Event-Triggered State Estimation for a Class of Delayed Recurrent Neural Networks with Sampled-Data Information

The paper investigates the state estimation problem for a class of recurrent neural networks with sampled-data information and time-varying delays. The main purpose is to estimate the neuron states through output sampled measurement; a novel event-triggered scheme is proposed, which can lead to a significant reduction of the information communication burden in the network; the feature of this scheme is that whether or not the sampled data should be transmitted is determined by the current sampled data and the error between the current sampled data and the latest transmitted data. By using a delayed-input approach, the error dynamic system is equivalent to a dynamic system with two different time-varying delays. Based on the Lyapunov-krasovskii functional approach, a state estimator of the considered neural networks can be achieved by solving some linear matrix inequalities, which can be easily facilitated by using the standard numerical software. Finally, a numerical example is provided to show the effectiveness of the proposed event-triggered scheme

Non-fragile state estimation for discrete Markovian jumping neural networks

In this paper, the non-fragile state estimation problem is investigated for a class of discrete-time neural networks subject to Markovian jumping parameters and time delays. In terms of a Markov chain, the mode switching phenomenon at different times is considered in both the parameters and the discrete delays of the neural networks. To account for the possible gain variations occurring in the implementation, the gain of the estimator is assumed to be perturbed by multiplicative norm-bounded uncertainties. We aim to design a non-fragile state estimator such that, in the presence of all admissible gain variations, the estimation error converges to zero exponentially. By adopting the Lyapunov–Krasovskii functional and the stochastic analysis theory, sufficient conditions are established to ensure the existence of the desired state estimator that guarantees the stability of the overall estimation error dynamics. The explicit expression of such estimators is parameterized by solving a convex optimization problem via the semi-definite programming method. A numerical simulation example is provided to verify the usefulness of the proposed methods

Delay-Dependent State Estimation of Static Neural Networks with Time-Varying and Distributed Delays

This paper focuses on studying the state estimation problem of static neural networks with time-varying and distributed delays. By constructing a suitable Lyapunov functional and employing two integral inequalities, a sufficient condition is obtained under which the estimation error system is globally asymptotically stable. It can be seen that this condition is dependent on the two kinds of time delays. To reduce the conservatism of the derived result, Wirtinger inequality is employed to handle a cross term in the time-derivative of Lyapunov functional. It is further shown that the design of the gain matrix of state estimator is transformed to finding a feasible solution of a linear matrix inequality, which is efficiently facilitated by available algorithms. A numerical example is explored to demonstrate the effectiveness of the developed result

Synchronization of decentralized event-triggered uncertain switched neural networks with two additive time-varying delays

This paper addresses the problem of synchronization for decentralized event-triggered uncertain switched neural networks with two additive time-varying delays. A decentralized eventtriggered scheme is employed to determine the time instants of communication from the sensors to the central controller based on narrow possible information only. In addition, a class of switched neural networks is analyzed based on the Lyapunov–Krasovskii functional method and a combined linear matrix inequality (LMI) technique and average dwell time approach. Some sufficient conditions are derived to guarantee the exponential stability of neural networks under consideration in the presence of admissible parametric uncertainties. Numerical examples are provided to illustrate the effectiveness of the obtained results.&nbsp

Modified Hopfield Neural Network Classification Algorithm For Satellite Images

Air adalah bahan yang penting bagi kehidupan mahkluk di atas muka bumi ini. Aktiviti manusia dan pengaruh alam semula jadi memberi kesan terhadap kualiti air, dan ia dianggap satu daripada masalah terbesar yang membelenggui kehidupan. Water is an essential material for living creatures. Human activities and natural influences have an effecting on water quality, and this is considered one of the largest problems facing living forms

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