多时滞随机神经网络的稳定性

通过构建李雅普偌夫函数的方法和利用半鞅收敛定理对一类随机时滞神经网络的全局指数稳定进行了分析,提出了易于判定随机时滞神经网络几乎必然指数稳定性新的代数判据,推广了[1]中的主要结论.     

Optimization of neural network for ionic conductivity of nanocomposite solid polymer electrolyte system (PEO-LiPF6-EC-CNT)

In this study, the ionic conductivity of a nanocomposite polymer electrolyte system (PEO-LiPF₆-EC-CNT), which has been produced using solution cast technique, is obtained using artificial neural networks approach. Several results have been recorded from experiments in preparation for the training and testing of the network. In the experiments, polyethylene oxide (PEO), lithium hexafluorophosphate (LiPF₆), ethylene carbonate (EC) and carbon nanotubes (CNT) are mixed at various ratios to obtain the highest ionic conductivity. The effects of chemical composition and temperature on the ionic conductivity of the polymer electrolyte system are investigated. Electrical tests reveal that the ionic conductivity of the polymer electrolyte system varies with different chemical compositions and temperatures. In neural networks training, different chemical compositions and temperatures are used as inputs and the ionic conductivities of the resultant polymer electrolytes are used as outputs. The experimental data is used to check the system’s accuracy following the training process. The neural network is found to be successful for the prediction of ionic conductivity of nanocomposite polymer electrolyte system.     

Predictive control of uncertain nonlinear parabolic PDE systems using a Galerkin/neural-network-based model

In this paper, a model predictive control (MPC) scheme for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities, arising in the context of transport-reaction processes, is proposed. A spatial operator of a parabolic PDE system is characterized by a spectrum that can be partitioned into a finite slow and an infinite fast complement. In this view, first, Galerkin method is used to derive a set of finite dimensional slow ordinary differential equation (ODE) system that captures the dominant dynamics of the initial PDE system. Then, a Multilayer Neural Network (MNN) is employed to parameterize the unknown nonlinearities in the resulting finite dimensional ODE model. Finally, a Galerkin/neural-network-based ODE model is used to predict future states in the MPC algorithm. The proposed controller is applied to stabilize an unstable steady-state of the temperature profile of a catalytic rod subject to input and state constraints.     

A dynamic system model for solving convex nonlinear optimization problems

This paper proposes a feedback neural network model for solving convex nonlinear programming (CNLP) problems. Under the condition that the objective function is convex and all constraint functions are strictly convex or that the objective function is strictly convex and the constraint function is convex, the proposed neural network is proved to be stable in the sense of Lyapunov and globally convergent to an exact optimal solution of the original problem. The validity and transient behavior of the neural network are demonstrated by using some examples.     

Hopfield neural networks in large-scale linear optimization problems

Hopfield neural networks and affine scaling interior point methods are combined in a hybrid approach for solving linear optimization problems. The Hopfield networks perform the early stages of the optimization procedures, providing enhanced feasible starting points for both primal and dual affine scaling interior point methods, thus facilitating the steps towards optimality. The hybrid approach is applied to a set of real world linear programming problems. The results show the potential of the integrated approach, indicating that the combination of neural networks and affine scaling interior point methods can be a good alternative to obtain solutions for large-scale optimization problems.     

Interpolation and rates of convergence for a class of neural networks

This paper presents a type of feedforward neural networks (FNNs), which can be used to approximately interpolate, with arbitrary precision, any set of distinct data in multidimensional Euclidean spaces. They can also uniformly approximate any continuous functions of one variable or two variables. By using the modulus of continuity of function as metric, the rates of convergence of approximate interpolation networks are estimated, and two Jackson-type inequalities are established.     

Definitions of equilibrium in network formation games

We examine a variety of stability and equilibrium definitions that have been used to study the formation of social networks among a group of players. In particular we compare variations on three types of definitions: those based on a pairwise stability notion, those based on the Nash equilibria of a link formation game, and those based on equilibria of a link formation game where transfers are possible.Bloch is also affiliated with the University of Warwick.     

Precision of neural timing: The small ? limit

We explore the precision of neural timing in a model neural system with n identical input neurons whose firing time in response to stimulation is chosen from a density f. These input neurons stimulate a target cell which fires when it receives m hits within ? msec. We prove that the density of the firing time of the target cell converges as ?→0 to the input density f raised to the mth and normalized. We give conditions for convergence of the density in L¹, pointwise, and uniformly as well as conditions for the convergence of the standard deviations.     

A note on the paper “characterization of all optimal solutions and parametric maximal flows in networks” of G. Ruhe (optimization 16 (1985) 1, 51-61)

First it is shown that the implementation of the algorithm proposed in the considered paper may cause some problems if no further specification is made as to one of its steps. Secondly, such a specification is suggested.     

Asymptotic stability analysis in uncertain multi-delayed state neural networks via Lyapunov–Krasovskii theory

This paper presents a new approach to the analysis of asymptotic stability of artificial neural networks (ANN) with multiple time-varying delays subject to polytope-bounded uncertainties. This approach is based on the Lyapunov–Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) technique with the use of a recent Leibniz–Newton model based transformation without including any additional dynamics.Three examples with numerical simulations are used to illustrate the effectiveness of the proposed method. The first example considers the neural network with multiple time-varying delays, which may be seen as a particular case of the second example where it is subject to uncertainties and multiple time-varying delays. Finally, the third example analyzes the stability of the neural network with higher numbers of neurons subject to a single time-delay. The Hopf bifurcation theory is used to verify the stability of the system when the origin falls into instability in the bifurcation point.