Cyclic Reformulation Based System Identification for Periodically Time-varying Systems
Hiroshi Okajima, Yusuke Fujimoto, Hiroshi Oku, Haruto Kondo
TL;DR
This work targets the identification of discrete-time linear periodically time-varying (LPTV) systems from input-output data without requiring periodic excitation. It introduces a cyclic reformulation that converts the M-periodic plant into an equivalent time-invariant representation using cycled signals, enabling a subspace identification (e.g., N4SID) to estimate an LTI model, which is then transformed via a state-coordinate transformation to recover the original cyclic parameters A_k, B_k, C_k, D_k. The approach yields a principled method to obtain the periodic system parameters from cycled-data identification, backed by a theoretical framework and numerical demonstrations showing high accuracy (even with process noise) in recovering the true P_ex parameters. This technique broadens practical capabilities for identifying LPTV systems without specialized periodic inputs, with potential impact in control and signal processing domains involving periodic dynamics.
Abstract
This paper addresses a system identification for linear periodically time-varying plants in the discrete-time setting. A system identification algorithm for linear, periodically time-varying plants is introduced based on a cyclic reformulation and a state coordinate transformation of the cycled system. By using our system identification algorithm, the high-accuracy model of the periodically time-varying plant can be obtained without using specific periodic input signals. The effectiveness of the proposed algorithm is demonstrated with numerical examples.