Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2006 Elsevier Ltd.This Letter is concerned with the global asymptotic stability analysis problem for a class of uncertain stochastic Hopfield neural networks with discrete and distributed time-delays. By utilizing a Lyapunov–Krasovskii functional, using the well-known S-procedure and conducting stochastic analysis, we show that the addressed neural networks are robustly, globally, asymptotically stable if a convex optimization problem is feasible. Then, the stability criteria are derived in terms of linear matrix inequalities (LMIs), which can be effectively solved by some standard numerical packages. The main results are also extended to the multiple time-delay case. Two numerical examples are given to demonstrate the usefulness of the proposed global stability condition.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, and the Alexander von Humboldt Foundation of Germany

Dynamics analysis and applications of neural networks

Ph.DDOCTOR OF PHILOSOPH

A methodology for neural spatial interaction modelling

This paper presents a methodology for neural spatial interaction modelling. Particular emphasis is laid on design, estimation and performance issues in both cases, unconstrained and singly constrained spatial interaction. Families of classical neural network models, but also less classical ones such as product unit neural network models are considered. Some novel classes of product unit and summation unit models are presented for the case of origin or destination constrained spatial interaction flows. The models are based on a modular connectionist architecture that may be viewed as a linked collection of functionally independent neural modules with identical feedforward topologies, operating under supervised learning algorithms. Parameter estimation is viewed as Maximum Likelihood (ML) learning. The nonconvex nature of the loss function makes the Alopex procedure, a global search procedure, an attractive and appropriate optimising scheme for ML learning. A benchmark comparison against the classical gravity models illustrates the superiority of both, the unconstrained and the origin constrained, neural network model versions in terms of generalization performance measured by Kullback and Leibler`s information criterion. Hereby, the authors make use of the bootstrapping pairs approach to overcome the largely neglected problem of sensitivity to the specific splitting of the data into training, internal validation and testing data sets, and to get a better statistical picture of prediction variability of the models. Keywords: Neural spatial interaction models, origin constrained or destination constrained spatial interaction, product unit network, Alopex procedure, boostrapping, benchmark performance tests.

Model Building and Optimization Analysis of MDF Continuous Hot-Pressing Process by Neural Network

We propose a one-layer neural network for solving a class of constrained optimization problems, which is brought forward from the MDF continuous hot-pressing process. The objective function of the optimization problem is the sum of a nonsmooth convex function and a smooth nonconvex pseudoconvex function, and the feasible set consists of two parts, one is a closed convex subset of Rn, and the other is defined by a class of smooth convex functions. By the theories of smoothing techniques, projection, penalty function, and regularization term, the proposed network is modeled by a differential equation, which can be implemented easily. Without any other condition, we prove the global existence of the solutions of the proposed neural network with any initial point in the closed convex subset. We show that any accumulation point of the solutions of the proposed neural network is not only a feasible point, but also an optimal solution of the considered optimization problem though the objective function is not convex. Numerical experiments on the MDF hot-pressing process including the model building and parameter optimization are tested based on the real data set, which indicate the good performance of the proposed neural network in applications

Nonlinear Systems

Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems