中文摘要：

针对回声状态网络存在的病态解以及模型规模控制问题，本文提出一种基于L1范数正则化的改进回声状态网络。该方法通过在目标函数中添加L1范数惩罚项，提高模型求解的数值稳定性，同时借助于L1范数正则化的特征选择能力，控制网络的复杂程度，防止出现过拟合。对于L1范数正则化的求解，采用最小角回归算法计算正则化路径，通过贝叶斯信息准则进行模型选择，避免估计正则化参数。将模型应用于人造数据和实际数据的时间序列预测中，仿真结果证明了本文方法的有效性和实用性。

英文摘要：

Considering the ill-posed problem and the model scale control of echo state network, an improved echo state network based on L1-norm regularization is proposed. In order to improve the numerical stability, the proposed method adds an L1-norm penalty term in the objective function. Meanwhile, the method can also control the complexity of the network and prevent overfitting by using feature selection capability of L1-norm regularization. To solve the L1-norm regularization model, we adopt the least angle regression algorithm to calculate regularization path and select suitable model through Bayesian information criterion, which can avoid the estimations of regularization parameter. The model is applied to the time series predictions of both synthetic dataset and practical dataset. The simulation results show the effectiveness and practicality of the proposed method.