二阶神经网络的全局指数稳定性分析

当神经网络应用于最优化计算时,理想的情形是只有一个全局渐近稳定的平衡点,并且以指数速度趋近于平衡点,从而减少神经网络所需计算时间,二阶神经网络较一般神经网络具有更快的收敛速度,对于二阶连续型Hopfield神经网络,用Lyapunov方法讨论平衡点的全局指数稳定性,给出了平衡点全局指数稳定的几个判别准则,作为特例,获得了连续型Hopfield神经网络全局指数稳定的新判据。

ANALYSIS OF GLOBAL EXPONENTIAL STABILITY OF SECOND ORDER NEURAL NETWORKS

When the neural network applies to optimal calculation, the ideal situation is that there is a unique equilibrium point which is globally asymptotically stable and the neural network tends to the equilibrium point at the speed of exponent. This can reduce the calculation time. The second order neural networks have faster convergence rate than the ordinary neural networks. Global exponential stability of equilibrium point for a class of second order Hopfield type neural networks is discussed by the Lyapunov method. Some criteria for global exponential stability of equilibrium point are obtained. As a special case, several new global exponential stability criteria are obtained for the corresponding Hopfield neural networks.