Adaptive regularised kernel-based identification method for large-scale systems with unknown order

Abstract

Regularised kernel-based identification methods are widely used for large-scale systems with the aim of reducing high parameter estimation variances. Classical diagonal and diagonal/correlated methods are used to design a kernel matrix under the assumption that the parameter series decays exponentially. This assumption has the following limitations: (1) if the system has an unknown time-delay/order, some irregular parameter sub-vectors are equal to zero vectors; (2) if the parameters have random structures, the parameter series does not decay exponentially. To address these limitations, an adaptive regularised kernel-based method is developed in this study. The basic idea is to set the values of diagonal elements of the kernel matrix based on the inner products between the output set and information vectors. Ultimately, the objective is to guarantee that a larger parameter corresponds to a smaller diagonal element. The proposed method can identify large-scale systems with high estimation accuracy. Simulation results demonstrate the effectiveness of the proposed method.