回响状态网络输出连接权重的一个稳定训练方法

Stable training method for output connection weights of echo state networks

鉴于在回响状态网络(ESN)的应用中常使用Wiener-Hopf方程学习输出连接权重,但该方法难以保证自治ESN的稳定性,首先分析了导致该稳定性丧失的原因,提出并证明了自治ESN具备Lyapunov稳定性的一个充分条件;然后将输出连接权重学习问题转化为一个非线性约束的最优化问题,并采用粒子群优化算法求解.仿真结果表明,所提方法既能确保ESN获取高精度的预测输出,又能保ESN的Lyapunov稳定性.

In applications of echo state network （ESN）, the Wiener-Hopf equation is usually used to learn the ESN＇s output connect weights, but can hardly ensure the stability of the autonomous ESNs. Therefore, The reasons for the loss of the stability are analyzed firstly, and a sufficient condition of the Lyapunov stability for the autonomous ESNs is proposed and proved. Then the output connect weight learning problem is. translated into an optimization problem with a nonlinear constraint. Particle swarm optimization algorithm is employed to solve the optimization problem. Finally, the simulation results show that the method proposed can not only result in high-precision prediction outputs of the ESN, but also ensure its Lyapunov stability.