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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.
Since the Wiener-Hopf equation is often used to study the output connection weight in the application of the Echo Network (ESN), it is difficult to guarantee the stability of the autonomous ESN. Firstly, the reasons for the loss of stability are analyzed. Lyapunov stability is considered. Then the output connection weight learning problem is transformed into a non-linear constrained optimization problem and solved by particle swarm optimization algorithm. The simulation results show that the proposed method not only ensures that ESN can obtain high-precision prediction Output, but also to ensure the Lyapunov stability ESN.