An Efficient Implementation for Kernel-based Regularized System Identification with Periodic Input Signals

Efficient implementation of algorithms for kernelbased regularized system identification is an important issue. The state of art result is based on semiseparable kernels and a class of commonly used test input signals in system identification and automatic control, and with such input signals, the output kernel is semiseparable and exploring this structure gives rise to very efficient implementation. In this paper, we consider instead the periodic input signal, which is another class of commonly used test input signals. Unfortunately, with periodic input signals, the output kernel is NOT semiseparable. Nevertheless, it can be shown that the output kernel matrix is hierarchically semiseparable. Moreover, it is possible to develop efficient implementation of algorithms by exploring the hierarchically semiseparable structure of the output kernel matrix and the periodic and Toeplitz structure of the regression matrix. The efficiency of the proposed implementation of algorithms is demonstrated by Monte Carlo simulations.