Nonlinear systems identification using dynamic multi-time scale neural networks

In this paper, two Neural Network (NN) identifiers are proposed for nonlinear systems identification via dynamic neural networks with different time scales including both fast and slow phenomena. The first NN identifier uses the output signals from the actual system for the system identification. The on-line update laws for dynamic neural networks have been developed using the Lyapunov function and singularly perturbed techniques. In the second NN identifier, all the output signals from nonlinear system are replaced with the state variables of the neuron networks. The on-line identification algorithm with dead-zone function is proposed to improve nonlinear system identification performance. Compared with other dynamic neural network identification methods, the proposed identification methods exhibit improved identification performance. Three examples are given to demonstrate the effectiveness of the theoretical results.     

基于神经网络的机器人运动模型辨识及其实验研究

针对机器人楚模中不确定因素的影响，采用神经网络辨识机器人输入输出间的非线性关系，建立机器人的运动学模型，为了提高神经网络的辨识速度，基于Elman动态递归网络，通过增加网络输入输出的部分信息，提出一种新的动态神经网络结构——状态廷迟输入动态递归神经网络(SDIDRNN)，提高了网络的学习速度和稳态精度。以PowerCube^TM模块化机器人为研究对象，把根据机器人返回的关节位置信息和利用OPTOTRAK3020三维运动测量系统测得的机器人末端位置信患作为SDIDRNN的学习样本，对包含各种影响因素的机器人运动模型进行辨识，得到了满意的结果，说明了该神经网络的优越性。     

Stability analysis for stochastic BAM neural networks with Markovian jumping parameters

This paper is concerned with the stability analysis issue for stochastic delayed bidirectional associative memory (BAM) neural network with Markovian jumping parameters. Assume that the jumping parameters are generated from continue-time discrete-state homogeneous Markov process and the delays are time-invariant. By employing the Lyapunov stability theory, some inequality techniques and the stochastic analysis, sufficient conditions are derived to achieve the global exponential stability in the mean square of the stochastic BAM neural network. One example is also provided in the end of this paper to illustrate the effectiveness of our results.     

Modeling and prediction with a class of time delay dynamic neural networks

In this paper, we propose a time delay dynamic neural network (TDDNN) to track and predict a chaotic time series systems. The application of artificial neural networks to dynamical systems has been constrained by the non-dynamical nature of popular network architectures. Many of the drawbacks caused by the algebraic structures can be overcome with TDDNNs. TDDNNs have time delay elements in their states. This approach provides the natural properties of physical systems. The minimization of a quadratic performance index is considered for trajectory tracking applications. Gradient computations are presented based on adjoint sensitivity analysis. The computational complexity is significantly less than direct method, but it requires a backward integration capability. We used Levenberg–Marquardt parameter updating method.     

Structure identification of uncertain general complex dynamical networks with time delay

It is well known that many real-world complex networks have various uncertain information, such as unknown or uncertain topological structure and node dynamics. The structure identification problem has theoretical and practical importance for uncertain complex dynamical networks. At the same time, time delay often appears in the state variables or coupling coefficients of various practical complex networks. This paper initiates a novel approach for simultaneously identifying the topological structure and unknown parameters of uncertain general complex networks with time delay. In particular, this method is also effective for uncertain delayed complex dynamical networks with different node dynamics. Moreover, the proposed method can be easily extended to monitor the on-line evolution of network topological structure. Finally, three representative examples are then given to verify the effectiveness of the proposed approach.     

Stabilization of stochastic Hopfield neural network with distributed parameters

In this paper, the stability of stochastic Hopfield neural network with distributed parameters is studied. To discuss the stability of systems, the main idea is to integrate the solution to systems in the space variable. Then, the integration is considered as the solution process of corresponding neural networks described by stochastic ordinary differential equations. A Lyapunov function is constructed and Ito formula is employed to compute the derivative of the mean Lyapunov function along the systems, with respect to the space variable. It is difficult to treat stochastic systems with distributed parameters since there is no corresponding Ito formula for this kind of system. Our method can overcome this difficulty. Till now, the research of stability and stabilization of stochastic neural networks with distributed parameters has not been considered.     

Global robust stability of delayed neural networks with a class of general activation functions

In this paper, the global robust stability is discussed for delayed neural networks with a class of general activation functions. By constructing new Lyapunov functionals, several novel conditions are derived to guarantee the existence, uniqueness and global robust stability of the equilibrium of neural networks with time delays. These conditions do not require the activation functions to be differentiable, bounded or monotonically nondecreasing. The results obtained here are generalizations of some earlier results reported in the literature for neural networks with time delays. In addition, two examples are given to illustrate our proposed results.     

Use of neural networks for predictions using time series: Illustration with the El Niño Southern oscillation phenomenon

This paper introduces the use of sets of multiple networks (bundled networks) to manage the variability due to different initialization parameters. This method makes it statistically impossible for the networks to be trapped in the same local minimum, and therefore allows better control of the confidence of the prediction eventually given. The spread of the forecasts given by these different networks can be used for prediction reliability purposes. An illustration of this usage is given with the El Niño phenomenon.     

Dynamical behaviour analysis of delayed complex-valued neural networks with impulsive effect

This paper investigates the problem of the dynamical behaviours of a class of complex-valued neural networks with mixed time delays and impulsive effect. By separating the complex-valued neural networks into the real and the imaginary parts, the corresponding equivalent real-valued systems are obtained. Some sufficient conditions are derived for assuring the exponential stability of the equilibrium point of the system based on the vector Lyapunov function method and mathematical induction method. The obtained results generalise the existing ones. Finally, two numerical examples with simulations are given to demonstrate the feasibility of the proposed results.     

A study on the use of statistical tests for experimentation with neural networks: Analysis of parametric test conditions and non-parametric tests

In this paper, we focus on the experimental analysis on the performance in artificial neural networks with the use of statistical tests on the classification task. Particularly, we have studied whether the sample of results from multiple trials obtained by conventional artificial neural networks and support vector machines checks the necessary conditions for being analyzed through parametrical tests. The study is conducted by considering three possibilities on classification experiments: random variation in the selection of test data, the selection of training data and internal randomness in the learning algorithm.The results obtained state that the fulfillment of these conditions are problem-dependent and indefinite, which justifies the need of using non-parametric statistics in the experimental analysis.     

Global exponential stability of neural networks with discrete and distributed delays and general activation functions on time scales

By employing time scale calculus theory, free weighting matrix method and linear matrix inequality (LMI) approach, several delay-dependent sufficient conditions are obtained to ensure the existence, uniqueness and global exponential stability of the equilibrium point for the neural networks with both infinite distributed delays and general activation functions on time scales. Both continuous-time and discrete-time neural networks are described under the same framework by the reported method. Illustrated numerical examples are given to show the effectiveness of the theoretical analysis. It is noteworthy that the activation functions are assumed to be neither bounded nor monotone.