In this paper, a primal-dual neural network based on linear variational inequalities (LVI) is presented for the online repetitive motion planning of PA10 robot arm, a kinematically redundant manipulator. To do this, a drift-free criterion is exploited. In addition, the physical constraints such as joint limits and joint velocity limits are incorporated into the problem formulation of such a redundancy-resolution scheme. The scheme is finally reformulated as a quadratic-programming (QP) problem. As a QP real-time solver, the LVI-based primal-dual neural network is designed based on the QP-LVI conversion and Karush-Kuhn-Tucker (KKT) condition. With simple piecewise-linear dynamics and global exponential convergence to optimal solutions, it can handle general QP and linear programming (LP) problems in the same inverse-free manner. The repetitive motion planning scheme and the LVI-based primal-dual neural network are simulated successfully based on PA10 robot arm, with effectiveness demonstrated.

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.

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）。

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。

The Wang neural network, together with its improved circuit implementation, could solve online a set of simultaneous linear equations. Global exponential convergence is presented for the Wang neural network, compared to the previously-presented asymptotical convergence. In addition, global stability results are presented for the Wang neural network. Illustrative examples further demonstrate the characteristics of the Wang neural network.