本论文揭示，作为两种并行的神经计算模型，BP和Hopfield类型神经网络都可以有效地对二次型V（x）=T/2+TVxxPxqx实现最小化求解。而且，尽管BP和Hopfield类型神经网络在网络设计思想和网络结构上呈现出很大的差异，但是它们在二次型函数最小化问题上都表现出了相同的学习能力，这说明两者具有本质的联系。

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.

A quadratic performance index is investigated for the online neural remedy for drift phenomenon of redundant robot manipulators. Computer simulations performed based on a three-link planar robot arm show the efficacy of such a quadratic-index based neural-remedy scheme.

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.

近年来，国内外学者发表了许多关于线性代数问题实时求解的方法，其中包括了矩阵求逆和线性方程组的并行求解方法。在研究了基于梯度法的递归神经网络用于Sylvester矩阵方程的实时求解后，通过使用Kronecker乘积和矩阵向量化等技术进行了MATLAB仿真从而验证了相关理论分析。计算机仿真的结果证实了这类神经网络方法在解决Sylvester矩阵方程中的有效性和高效率（特别是在使用幂S型激励函数的情况下）。