Exponential H∞ synchronization and state estimation for chaotic systems via a unified model

In this paper, H∞ synchronization and state estimation problems are considered for different types of chaotic systems. A unified model consisting of a linear dynamic system and a bounded static nonlinear operator is employed to describe these chaotic systems, such as Hopfield neural networks, cellular neural networks, Chua's circuits, unified chaotic systems, Qi systems, chaotic recurrent multilayer perceptrons, etc. Based on the H∞ performance analysis of this unified model using the linear matrix inequality approach, novel state feedback controllers are established not only to guarantee exponentially stable synchronization between two unified models with different initial conditions but also to reduce the effect of external disturbance on the synchronization error to a minimal H∞ norm constraint. The state estimation problem is then studied for the same unified model, where the purpose is to design a state estimator to estimate its states through available output measurements so that the exponential stability of the estimation error dynamic systems is guaranteed and the influence of noise on the estimation error is limited to the lowest level. The parameters of these controllers and filters are obtained by solving the eigenvalue problem. Most chaotic systems can be transformed into this unified model, and H∞ synchronization controllers and state estimators for these systems are designed in a unified way. Three numerical examples are provided to show the usefulness of the proposed H∞ synchronization and state estimation conditions.

Adaptive pinning control of deteriorated nonlinear coupling networks with circuit realization

This paper deals with a class of complex networks with nonideal coupling networks, and addresses the problem of asymptotic synchronization of the complex network through designing adaptive pinning control and coupling adjustment strategies. A more general coupled nonlinearity is considered as perturbations of the network, while a serious faulty network named deteriorated network is also proposed to be further study. For the sake of eliminating these adverse impacts for synchronization, indirect adaptive schemes are designed to construct controllers and adjusters on pinned nodes and nonuniform couplings of un-pinned nodes, respectively. According to Lyapunov stability theory, the proposed adaptive strategies are successful in ensuring the achievement of asymptotic synchronization of the complex network even in the presence of perturbed and deteriorated networks. The proposed schemes are physically implemented by circuitries and tested by simulation on a Chua's circuit network.

H∞ State Estimation for Discrete-Time Chaotic Systems Based on a Unified Model

This paper is concerned with the problem of state estimation for a class of discrete-time chaotic systems with or without time delays. A unified model consisting of a linear dynamic system and a bounded static nonlinear operator is employed to describe these systems, such as chaotic neural networks, Chua's circuits, Hénon map, etc. Based on the H∞ performance analysis of this unified model using the linear matrix inequality approach, H∞ state estimator are designed for this model with sensors to guarantee the asymptotic stability of the estimation error dynamic systems and to reduce the influence of noise on the estimation error. The parameters of these filters are obtained by solving the eigenvalue problem. As most discrete-time chaotic systems with or without time delays can be described with this unified model, H∞ state estimator design for these systems can be done in a unified way. Three numerical examples are exploited to illustrate the effectiveness of the proposed estimator design schemes.

Smoothing neural network for constrained non-Lipschitz optimization with applications

In this paper, a smoothing neural network (SNN) is proposed for a class of constrained non-Lipschitz optimization problems, where the objective function is the sum of a nonsmooth, nonconvex function, and a non-Lipschitz function, and the feasible set is a closed convex subset of . Using the smoothing approximate techniques, the proposed neural network is modeled by a differential equation, which can be implemented easily. Under the level bounded condition on the objective function in the feasible set, we prove the global existence and uniform boundedness of the solutions of the SNN with any initial point in the feasible set. The uniqueness of the solution of the SNN is provided under the Lipschitz property of smoothing functions. We show that any accumulation point of the solutions of the SNN is a stationary point of the optimization problem. Numerical results including image restoration, blind source separation, variable selection, and minimizing condition number are presented to illustrate the theoretical results and show the efficiency of the SNN. Comparisons with some existing algorithms show the advantages of the SNN.

Stochastic competitive learning in complex networks

Competitive learning is an important machine learning approach which is widely employed in artificial neural networks. In this paper, we present a rigorous definition of a new type of competitive learning scheme realized on large-scale networks. The model consists of several particles walking within the network and competing with each other to occupy as many nodes as possible, while attempting to reject intruder particles. The particle's walking rule is composed of a stochastic combination of random and preferential movements. The model has been applied to solve community detection and data clustering problems. Computer simulations reveal that the proposed technique presents high precision of community and cluster detections, as well as low computational complexity. Moreover, we have developed an efficient method for estimating the most likely number of clusters by using an evaluator index that monitors the information generated by the competition process itself. We hope this paper will provide an alternative way to the study of competitive learning..

Distributed state estimation for discrete-time sensor networks with randomly varying nonlinearities and missing measurements

This paper deals with the distributed state estimation problem for a class of sensor networks described by discrete-time stochastic systems with randomly varying nonlinearities and missing measurements. In the sensor network, there is no centralized processor capable of collecting all the measurements from the sensors, and therefore each individual sensor needs to estimate the system state based not only on its own measurement but also on its neighboring sensors' measurements according to certain topology. The stochastic Brownian motions affect both the dynamical plant and the sensor measurement outputs. The randomly varying nonlinearities and missing measurements are introduced to reflect more realistic dynamical behaviors of the sensor networks that are caused by noisy environment as well as by probabilistic communication failures. Through available output measurements from each individual sensor, we aim to design distributed state estimators to approximate the states of the networked dynamic system. Sufficient conditions are presented to guarantee the convergence of the estimation error systems for all admissible stochastic disturbances, randomly varying nonlinearities, and missing measurements. Then, the explicit expressions of individual estimators are derived to facilitate the distributed computing of state estimation from each sensor. Finally, a numerical example is given to verify the theoretical results.

Delay-distribution-dependent state estimation for discrete-time stochastic neural networks with random delay

This paper is concerned with the state estimation problem for a class of discrete-time stochastic neural networks (DSNNs) with random delays. The effect of both variation range and distribution probability of the time delay are taken into account in the proposed approach. The stochastic disturbances are described in terms of a Brownian motion and the time-varying delay is characterized by introducing a Bernoulli stochastic variable. By employing a Lyapunov-Krasovskii functional, sufficient delay-distribution-dependent conditions are established in terms of linear matrix inequalities (LMIs) that guarantee the existence of the state estimator which can be checked readily by the Matlab toolbox. The main feature of the results obtained in this paper is that they are dependent on not only the bound but also the distribution probability of the time delay, and we obtain a larger allowance variation range of the delay, hence our results are less conservative than the traditional delay-independent ones. One example is given to illustrate the effectiveness of the proposed result.

Missing value imputation on missing completely at random data using multilayer perceptrons

Data mining is based on data files which usually contain errors in the form of missing values. This paper focuses on a methodological framework for the development of an automated data imputation model based on artificial neural networks. Fifteen real and simulated data sets are exposed to a perturbation experiment, based on the random generation of missing values. These data set sizes range from 47 to 1389 records. A perturbation experiment was performed for each data set where the probability of missing value was set to 0.05. Several architectures and learning algorithms for the multilayer perceptron are tested and compared with three classic imputation procedures: mean/mode imputation, regression and hot-deck. The obtained results, considering different performance measures, not only suggest this approach improves the quality of a database with missing values, but also the best results are clearly obtained using the Multilayer Perceptron model in data sets with categorical variables. Three learning rules (Levenberg-Marquardt, BFGS Quasi-Newton and Conjugate Gradient Fletcher-Reeves Update) and a small number of hidden nodes are recommended.

Computation of synchronized periodic solution in a BAM network with two delays

A bidirectional associative memory (BAM) neural network with four neurons and two discrete delays is considered to represent an analytical method, namely, perturbation-incremental scheme (PIS). The expressions for the periodic solutions derived from Hopf bifurcation are given by using the PIS. The result shows that the PIS has higher accuracy than the center manifold reduction (CMR) with normal form for the values of time delay not far away from the Hopf bifurcation point. In terms of the PIS, the necessary and sufficient conditions of synchronized periodic solution arising from a Hopf bifurcation are obtained and the synchronized periodic solution is expressed in an analytical form. It can be seen that theoretical analysis is in good agreement with numerical simulation. It implies that the provided method is valid and the obtained result is correct. To the best of our knowledge, the paper is the first one to introduce the PIS to study the periodic solution derived from Hopf bifurcation for a 4-D delayed system quantitatively.