基于函数逼近理论，构造一种Chebyshev基函数神经网络模型。推导出该网络模型的权值直接确定方法，可一步计算出权值，克服了传统BP神经网络学习率选取困难、学习过程冗长和易陷入局部极小等缺点。在此基础上，设计了基于二分搜索的结构自适应算法，根据精度要求自动确定网络最优结构。理论分析及仿真验证均表明，该网络不仅能够快速地完成网络权值确定和结构自适应，且具有优异的学习与逼近能力，而且对随机加性噪声也具有较好的抑制作用。

本文利用优化方法及递归神经网络实时求解器消除冗余机器手臂在运动过程中出现的角偏差问题。鉴于机器手臂都存在着关节物理约束，我们的优化方案也因此考虑关节极限和关节速度极限的躲避。更重要的是，本文详细分析了该成功解决关节角偏差问题的二次型性能指标的设计原理。仿真结果证实了该方法的可行性与有效性。

In view of parallel-processing nature and circuit-implementation convenience, recurrent neural networks are often employed to solve optimization problems. Recently, a primal-dual neural network based on linear variational inequalities (LVI) was developed by Zhang et al. for the online solution of linear-programming (LP) and quadratic-programming (QP) problems simultaneously subject to equality, inequality and bound constraints. For the final purpose of field programmable gate array (FPGA) and application-specific integrated circuit (ASIC) realization, we investigate in this paper the MATLAB Simulink modeling and simulative verification of such an LVI-based primal-dual neural network (LVI-PDNN). By using click-and-drag mouse operations in MATLAB Simulink environment, we could quickly model and simulate complicated dynamic systems. Modeling and simulative results substantiate the theoretical analysis and efficacy of the LVI-PDNN for solving online the linear and quadratic programs.

A gradient neural network (CNN) for solving online a set of simultancous linsr equations is gencralized and investigated in this paper. Instead if the carlier-prcesented asymptotical convergence, global exponontial convergence could be proved for such a class of ncural networks, In addition, superior convergcnce could be achicved using power-sigmoid avtivation-funcitionsm, compared with tiing lincar activation-functions Computer-simulation results substantiate further the above analysis and efficacy of such neural network.

In this Letter, by following Zhang et al. is method, a recurrent neural network (termed as Zhang neural network, ZNN) is developed and analyzed for solving online the time-varying convex quadraticprogramming problem subject to time-varying linear-equality constraints. Different from conventional gradient-based neural networks (GNN), such a ZNN model makes full use of the time-derivative information of time-varying coefficient. The resultant ZNN model is theoretically proved to have global exponential convergence to the time-varying theoretical optimal solution of the investigated time-varying convex quadratic program. Computer-simulation results further substantiate the effectiveness, efficiency and novelty of such ZNN model and method.