Identification of Nonlinear Systems via LPV Model Identification Around a Time-Varying Trajectory

Abstract

Nonlinear (NL) systems are appearing in all engineering applications. Deriving models for these systems is important for instance for prediction and control. The goal of this paper is to estimate models of a class of NL systems via linearization around a time-varying setpoint. By considering one stable trajectory of the NL system, the system can be approximated by a linear parameter-varying (LPV) model around this trajectory. Indeed, this LPV model is the NL system linearized around the trajectory, which we will identify by perturbing the trajectory. After the identification of the LPV model, we reconstruct the NL system by symbolic integration of the estimated LPV coefficients. In this paper, we show that to guarantee the integrability of the LPV coefficients, the parametrization of this LPV model must have a specific structure which we will exploit for its identification. This structure shows that the parameter-varying (PV) coefficients of this LPV are related to each other. Finally, simulation results demonstrate the effectiveness of the proposed identification approach.