A Non-Parametric LPV Approach to the Indentification of Linear Periodic Systems

Abstract

Abstract A non-parametric identification algorithm is proposed to identify Linear Time Periodic (LTP) systems. The period is unknown and can be any real positive number. The system is modelled as an ARX Linear Parameter Varying (LPV) system with a virtual scheduling signal consisting of two orthogonal sinusoids (a sine and a cosine) with a period equal to the system period. Hence, the system parameters are polynomial functions of the scheduling vector. As these polynomials may have infinite degree, a non-parametric model is adopted to describe the LPV system. This model is identified by a Gaussian Process Regression (GPR) algorithm where the system period is a hyperparameter. The performance of the proposed identification algorithm is illustrated through the identification of a simulated LTP continuous system described by a state-space model. The ARX-LTP discrete-time model estimated in the noiseless case was taken as the true model.