Stability Analysis for Dynamical Neural Networks with Distributed Delays

Stochastic supply and fluctuating travel demand in transport systems leads to stochastic travel times and travel costs for travelers. This chapter will establish a dynamic road network design approach considering stochastic capacity and its influence on travelers’ choice behavior under uncertainty. This chapter will firstly work on the modeling of travelers’ departure time/route choice behavior under stochastic capacities. A reliability-based dynamic network design approach is proposed and formulated of which numbers of lanes on all the potential links are the design variables. A combined road network-oriented Genetic Algorithm and set evaluation algorithm is proposed to solve the dynamic network design problem. The proposed reliability-based dynamic network design approach is applied to a hypothetical network, and its solutions are compared to a corresponding static network design approach. It is concluded that the static network design approach may lead to inferior designs. In general static traffic assignment underestimates the overall total network travel time and total network travel costs. Dynamic network design approach appears to derive a fairly good allocation of road capacity over space and makes the best utilization of the network capacity over time.

In this paper the design of a dynamic neural network (DNN) for modeling and control of a class of minimum-phase controllable nonlinear systems is considered. The dynamic neural network acts as a generic model of the system, which is then used in the derivation of the control signal. The training of the network is based oil a novel scheme that arranges the outputs of the hidden layer of the DNN into a set of orthogonal basis functions. This allows for the derivation of a stable rule for the training of the DNN's weights and does not require random initialization of the weights.

Dynamic neural networks with different time-scales include the aspects of fast and slow phenomenons. Some applications require that the equilibrium points of the designed network be stable. In this paper, the passivity-based approach is used to derive stability conditions for dynamic neural networks with different time-scales. Several stability properties, such as passivity, asymptotic stability, input-to-state stability and bounded input bounded output stability, are guaranteed in certain senses. Numerical examples are also given to demonstrate the effectiveness of the theoretical results.

Dynamic neural networks with different time-scales include the aspects of fast and slow phenomenons. Some applications require that the equilibrium points of the designed networks are stable. In this paper, the passivity-based approach is used to derive stability conditions for dynamic neural networks with different time-scales. Several stability properties, such as passivity, asymptotic stability, input-to-state stability and bounded input bounded output stability, are guaranteed in certain senses. A numerical example is also given to demonstrate the effectiveness of the theoretical results.

This paper proposes and evaluates the application of a modular dynamic recurrent neural network (DRNN) to classify upper limb motion using myoelectric signals. The DRNN algorithmic issues, including the structure selection, the segmentation of the data and various feature sets such as time-domain features and frequency features, were evaluated experimentally in order to actualize the optimization and configuration of this classification scheme. This was achieved by using a majority vote technique to post-process the output decision stream. The DRNN-based approach was then been compared with two commonly used classification methods: multilayer perceptron (MLP) neural network and linear discriminant analysis (LDA). The DRNN-based motion classification system demonstrated exceptional accuracy and a low computational load for the classification of robust limb motion. The DRNN may also display utility for online training and controlling rehabilitation robots.

Paper focuses on the optimization of the advertising and other additional costs for the small business ecommerce web sites. The aim of this paper was to propose a dynamic neural network based algorithm to predict number of clicks on a particular advertising link in three web pages of three different small companies working in the same business segment. The dynamic neural network based algorithm was proposed for forecasting the upcoming values of the advertisement clicks. The best results of 10% average forecasting uncertainty was received for two layer NARX network with three additional inputs: bounce rate, average session time and average page load time. The application of NAR neural network without external inputs increased the forecasting uncertainty to 25% which is similar to received 26% LPC uncertainty.

Fundamental to a systematic synthesis of neural networks for optimization, associative memory and continuous mapping applications is a qualitative analysis of the network equilibrium conditions and the convergence of network trajectories to these equilibria. Specific conditions using the theory of P-matrices are developed in this paper for characterizing the equilibrium conditions and the stability properties for an important class of neural networks that has received wide attention. Network structures for ensuring equilibrium confinement are identified by determining conditions for uniqueness of stable equilibrium points in specified quadrants of the state space. Conditions on network parameters for ensuring exponential stability with an arbitrarily specified degree within the basins of attraction of the equilibrium points are also presented. These results serve as valuable guidelines in the synthesis of neural networks for any specific application.

An adaptive identification method of simple dynamic recurr ent neural network (SRNN) for nonlinear dynamic systems is presented in this paper. This method based on the theory that by using the inner-states feed-back of dynamic network to describe the nonlinear kinetic characteris tics of system can reflect the dynamic ch aracteristics more directly, deduces the recursive prediction error (RPE) learning algorithm of SRNNe and improves the algorithm by studying topological structure on recursion layer without the weight values. The simulation results indicate that this kind of neural network can be used in real-time control, due to its less weight values, simpler learning algorithm, higher identification speed, and higher precision of model. It solves the problems of intricate in training algorithm and slow rate in convergence caused by the complicate topologi cal structure in usual dynami c recurrent neural network. Keywords: non-linear system, system identification, dynamic recurrent neural network, RPE algorithm

This paper focuses on the design of a dynamic Petri recurrent fuzzy neural network (DPRFNN), and this network structure is applied to the path-tracking control of a nonholonomic mobile robot for verifying its validity. In the DPRFNN, the concept of a Petri net and the recurrent frame of internal-feedback loops are incorporated into a traditional FNN to alleviate the computation burden of parameter learning and to enhance the dynamic mapping of network ability. Moreover, the supervised gradient-descent method is used to develop the online-training algorithm for the DPRFNN control. In order to guarantee the convergence of path-tracking errors, analytical methods based on a discrete-type Lyapunov function are proposed to determine varied learning rates for DPRFNN. In addition, the effectiveness of the proposed DPRFNN control scheme under different moving paths is verified by experimental results, and its superiority is indicated in comparison with FNN, RFNN, Petri FNN, and PRFNN control systems.

Time-varying quadratic programming (TV-QP) is widely used in artificial intelligence, robotics, and many other fields. To solve this important problem, a novel discrete error redefinition neural network (D-ERNN) is proposed. By redefining the error monitoring function and discretization, the proposed neural network is superior to some traditional neural networks in terms of convergence speed, robustness, and overshoot. Compared with the continuous ERNN, the proposed discrete neural network is more suitable for computer implementation. Unlike continuous neural networks, this article also analyzes and proves how to select the parameters and step size of the proposed neural networks to ensure the reliability of the network. Moreover, how to achieve the discretization of the ERNN is presented and discussed. The convergence of the proposed neural network without disturbance is proven, and bounded time-varying disturbances can be resisted in theory. Furthermore, the comparison results with other related neural networks show that the proposed D-ERNN has a faster convergence speed, better antidisturbance ability, and lower overshoot.

Recurrent neural networks unlike feed-forward networks are able to process inputs with time context. The key role in this process is played by the dynamics of the network, which transforms input data to the recurrent layer states. Several authors have described and analyzed dynamics of small sized recurrent neural networks with two or three hidden units. In our work we introduce techniques that allow to visualize and analyze the dynamics of large recurrent neural networks with dozens units, reveal both stable and unstable points (attractors and saddle points), which are important to understand the principles of successful task processing. As a practical example of this approach, dynamics of the simple recurrent network trained by two different training algorithms on context-free language anbnwas studied.

A novel backpropagation learning algorithm for a particular class of dynamic neural networks in which some units have a local feedback is proposed. Hence these networks can be trained to respond to sequences of input patterns. This algorithm has the same order of space and time requirements as backpropagation applied to feedforward networks. The authors present experimental results and comparisons with a speech recognition problem. >

An increasing number of applications of dynamic neural networks has been developed for digital signal processing (DSP), dynamic neural networks are feedforward neural networks with commonly used scalar synapses replaced by linear filters. This provides feedforward neural networks with the capability of performing dynamic mappings, which depend on past input values, dynamic neural networks are suitable for time series prediction, nonlinear system identification, and signal processing applications. Their most popular types are Finite Impulse Response (FIR) neural networks, which are obtained by replacing synapses with finite impulse response filters. Due to their guaranteed stability characteristic and easy to minimize error surface they have been used with great success in many applications such as signal enhancement, noise cancellation, classification of input patterns, system identification, prediction, and control.. Most of the works on system identification using neural networks are based on multilayer feedforward neural networks with backpropagation learning or more efficient variations of this algorithm, an elegant method for training layered networks. This paper is based on work in a Dynamic System Modeling (DYSMO) and as an application for speed control of DC motor drive.

In this paper the development and application of a dynamic neural network called the dynamic neural processor (DNP) are discussed. The DNP is developed based on the neuro-physiological evidence that neural activity of any complexity depends upon the interaction of assembly of cells called neural subpopulations. A single subpopulation of neurons is assumed to consist of a number of similar neurons that lie in close proximity. For simplicity, live neural subpopulations, namely excitatory and inhibitory, are assumed to exist in a neural population. The DNP consists of two dynamic neurons configured to function as excitatory and inhibitory neurons. A learning algorithm to adapt the weights of the subpopulation and the connecting weights between the subpopulations is developed. The efficacy of the DNP structure is demonstrated for the direct adaptive control of unknown nonlinear systems. >

With the development of computer technology, quantitative investment based on data and rules has gradually emerged in China. Quantitative model has become a powerful tool to predict the market and guide investment. However, due to the complexity of the stock market, the traditional time series prediction technology has many shortcomings. The introduction of nonlinear autoregressive neural network NARX provides a basis for quantitative analysis of investment in stocks. The quantitative stock technical index data is taken as the training parameter and input parameter of NARX dynamic regression neural network, and the analysis results are obtained. We have collected Shanghai composite index data, tested the accuracy of quantitative analysis method, analyzed the prediction results of the model, compared the difference between the prediction results and the actual data so as to analyze the accuracy of the model. KeywordsNeural networkNARXQuantitative investment