Lagrange神经网络的稳定性分析

Stability analysis of Lagrange neural networks

若重新定义与不等式约束相关的乘子为正定函数,则在构造Lagrange神经网络时,可直接使用处理等式约束的方法处理不等式约束,不需再用松驰变量将不等式约束转换为等式约束,减小了网络实现的复杂程度.利用Liapunov一阶近似原理,严格分析了这类Lagrange神经网络的局部稳定性;并采用LaSalle不变集原理,讨论其大范围稳定性.

By redefining multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, it is no longer necessary to convert inequality constraints into equality constraints by slack variables in order to reuse the method dedicated to equality constraints for constructing Lagrange neural networks. The local stability of the Lagrange neural networks is proved rigorously with the first Liapunov approximation principle. The stability in the large is discussed based on the LaSalle invariance principle.