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.

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.

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。

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。

从控制工程的角度，概括介绍了作为国际互联网的最新核心技术之一的Java语言的特点和发展，并具体结合人工神经网络的仿真与实现，以实际例子论述其在科学研究中将发挥的巨大效用和带来的新思想。