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Determination of appropriate neural-network (NN) structure is an important issue for a given learning or training task since the NN performance depends much on it. To remedy the weakness of conventional BP neural networks and learning algorithms, a new Laguerre orthogonal basis neural network is constructed. Based on this special structure, a weights-direct-determination method is derived, which could obtain the optimal weights of such a neural network directly (or to say, just in one step). Furthermore, a growing algorithm is presented for determining immediately the smallest number of hidden-layer neurons. Theoretical analysis and simulation results substantiate the efficacy of such a Laguerre-orthogonal-basis neural network and its growing algorithm based on the weights-direct-determination method. [ABSTRACT FROM AUTHOR]

With the proved efficacy on solving linear time-varying matrix or vector equations, Zhang neural network (ZNN) could be generalized and developed for the online minimization of time-varying quadratic functions. The minimum of a time-varying quadratic function can be reached exactly and rapidly by using Zhang neural network, as compared with conventional gradient-based neural networks (GNN). Computer-simulation results substantiate further that ZNN models are superior to GNN models in the context of online time-varying quadratic function minimization. [ABSTRACT FROM AUTHOR]

This paper presents a new kind of recurrent neural network proposed by Zhang et al. for solving online Lyapunov equation with time-varying coefficient matrices. Global exponential convergence could be achieved by such a recurrent neural network when solving the time-varying problems in comparison with gradient neural networks (GNN). MATLAB simulation of both neural networks for the real-time solution of time-varying Lyapunov equation is then investigated through several important techniques. Computer-simulation results substantiate the theoretical analysis and demonstrate the efficacy of such a Zhang neural network (ZNN) on time-varying Lyapunov equation solving, especially when using power-sigmoid activation functions. [ABSTRACT FROM AUTHOR]

For online solution of nonlinear equation f(x) = 0, this paper generalizes a special kind of recurrent neural dynamics by using a recent design method proposed by Zhang et al. Different from gradient-based dynamics (GD), the resultant Zhang dynamics (ZD) is designed based on the elimination of an indefinite error-monitoring function (instead of the elimination of a square-based positive error-function usually associated with GD). For comparative purposes, the gradient-based dynamics is also developed and exploited for solving online such a nonlinear equation f(x) = 0. Computer-simulation results via power-sigmoid activation functions substantiate further the theoretical analysis and efficacy of Zhang neural dynamics on nonlinear equations solving. [ABSTRACT FROM AUTHOR]