为解决在速度层上无穷范数最小化模型中可能出现的不连续点问题，提出一种基于双判据方法的二次型优化模型。冗余机器人运动规划与控制模型可以统一各种关节物理极限，如关节变量极限与关节速度极限。同时该模型又可以最终转化为一个标准的二次规划问题。为了实时求解该二次规划问题，提出一种基于线性变分不等式（LVI）的原对偶神经网络。该神经网络作为实时求解器具有简单的分段线性结构和较高的计算效率。计算机对PUMA560机器手臂的模拟仿真表明，该方案具有灵活性和有效性。

One of state-of-the-art recurrent neural networks (RNN) is dual neural network (DNN). It can solve quadratic programs (QP) in real time. The dual neural network is of simple piecewise-linear dynamics and has global (exponential) convergence to optimal solutions. In this chapter, we firstly introduce the QP problem formulation and its online solution based on recurrent neural networks. Some related concepts and definitions are also given. Secondly, we present the dual neural network and its design method. In addition to the general design method, for non-diagonal, non-analytical and/or time-varying cases, a matrix-inverse neural network could be combined into such a design procedure of dual neural network for online computation of its matrixinverse related term. Thirdly, we show the analysis results of dual neural networks. In addition to the general analysis results, we investigate the proof complexity of the exponential convergence condition of dual neural networks. Fourthly, we present the numerical simulation and illustrative example of using the dual neural network to solve static QP problems. Finally, we exploit the dual neural network to online solve motion planning problems of redundant robot manipulators, which is illustrated as engineering-application examples.

简述了协处理器的概念、任务、发展历程和现状，探讨了协处理器之所以引起人们重视和再重视的原因及其优势，简单介绍和展望了如何用FPGA等类型协处理器构建高性能计算平台。

为避免权值反复迭代修正的冗长BP训练过程，避免传统方法陷入局部极小点，根据多项式理论，构造了一种新型前向神经网络模型，推导了基于最速下降法的误差反传算法和基于伪逆的直接确定法。仿真结果显示，迭代方法和伪逆直接确定法都能达到比较高的工作精度（10-6）。

以平方可积空间上的复指数Fourier级数作为激励函数构造了新型Fourier神经元网络，并推导出采用加号逆表示的网络权值直接确定公式，克服了传统BP神经网络收敛速度慢、易陷于局部极小点、迭代学习易发生振荡等缺陷。并在此基础上构造了隐神经元衍生算法，克服了传统BP神经网络难以确定最优网络拓扑结构的缺点。理论分析及仿真实验表明，该复指数Fourier神经元网络能够一步计算网络最优权值且能自适应调整网络结构，对随机加性噪声具有抑制作用，并能高精度逼近非连续函数。