Recurrent stochastic configuration networks (RSCNs) have shown great potential in modelling nonlinear dynamic systems with uncertainties. This paper presents an RSCN with hybrid regularization to enhance both the learning capacity and generalization performance of the network. Given a set of temporal data, the well-known least absolute shrinkage and selection operator (LASSO) is employed to identify the significant order variables. Subsequently, an improved RSCN with L2 regularization is introduced to approximate the residuals between the output of the target plant and the LASSO model. The output weights are updated in real-time through a projection algorithm, facilitating a rapid response to dynamic changes within the system. A theoretical analysis of the universal approximation property is provided, contributing to the understanding of the network's effectiveness in representing various complex nonlinear functions. Experimental results from a nonlinear system identification problem and two industrial predictive tasks demonstrate that the proposed method outperforms other models across all testing datasets.

翻译：循环随机配置网络（RSCNs）在建模具有不确定性的非线性动态系统方面展现出巨大潜力。本文提出一种具有混合正则化的RSCN，以增强网络的学习能力和泛化性能。给定一组时序数据，首先采用著名的LASSO（最小绝对收缩与选择算子）来识别重要的阶次变量。随后，引入一种改进的、带有L2正则化的RSCN来逼近目标对象输出与LASSO模型之间的残差。输出权重通过投影算法实时更新，从而促进对系统内部动态变化的快速响应。本文提供了对网络通用逼近性质的理论分析，有助于理解其在表示各种复杂非线性函数方面的有效性。在一个非线性系统辨识问题和两个工业预测任务上的实验结果表明，所提方法在所有测试数据集上均优于其他模型。