March 3, 2026Open Access

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

Key Points

The proposed approach enables identification of fractional-order systems with unknown initial conditions, demonstrating fast convergence.
Initial conditions were effectively modeled using a Luenberger observer, allowing for accurate frequency-distributed state estimation.
A combined initialization and identification procedure utilized Least Squares parameter estimation for both linear and nonlinear systems.
Illustrative examples show the significant reduction in parameter bias with the proposed two-stage identification methodology.

Abstract

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.

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

Key Points

Abstract

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