连续MFN神经控制系统的稳定性判据

A Stability Criterion of Continuous MFN Neural Control System

针对广泛应用的多层前向神经网络 (MFN) ,建立了连续MFN控制系统的数学模型 ,给出了其闭环稳定性判据 ,利用Lyapunov方法 ,进行了严格的数学证明 ,并且在证明过程中给出了系统的Lyapunov函数 ,同时进一步得出了系统为线性系统时的稳定性条件 ,最后讨论了目前神经控制系统稳定性研究中存在的有关问题 ,指出了将来的研究方向。

In this paper, a mathematical model of wide-existing continuous MFN (Multilayer Feed-forward Network) neural control system is established. The stability criterion of this system is proposed. And basing on Lyapunov method, strict mathematical demonstration is given. During the demonstration, the Lyapunov function of the system is also given. Then a corollary of the linear system is proposed. Finally, some existing problems of neural control system stability are discussed, and the future research direction is pointed out.