Initialization and Identification of Linear and Nonlinear FDEs with Unknown Initial Conditions: an Introduction

This paper presents a new methodology for identifying fractional-order systems with unknown initial conditions. The proposed approach is based on the Infinite State Representation framework, which is employed to model and estimate the frequency-distributed state of the fractional system using a Luenberger observer. A combined initialization and identification procedure enables Least Squares parameter estimation for both linear and nonlinear systems. Simple illustrative examples demonstrate the effectiveness of the proposed two-stage identification procedure, characterized by fast convergence and a significant reduction in parameter bias.