Kernel Regularization Based Volterra Series Identification Method for Time-delayed Nonlinear Systems with Unknown Structure

This paper develops a kernel regularization based Adam algorithm for nonlinear systems with unknown structure and time-delay by using self-organized maps. Based on the redundant rule method, a model pool constituted of several Volterra series is constructed which contains the true time-delayed model. Then, the Adam algorithm combining a self-organized maps technique is applied to iteratively estimate the time-delay and parameters. Furthermore, a kernel regularization method is introduced to deal with the curse of dimensionality, and by which a more simple Volterra model can be obtained. Experimental results show the effectiveness of proposed algorithm in estimating time-delay and parameters.