Identification method for a fractional-order system in terms of equivalent dynamic properties

Area of Science:

• Dynamical Systems
• Control Theory
• Applied Mathematics

Background:

• Fractional dynamic systems offer complex behaviors but are challenging to identify.
• Traditional methods focus on computational efficiency of fractional terms.
• Data-driven approaches for fractional system identification are needed.

Purpose of the Study:

• To develop an efficient, data-driven method for identifying fractional dynamic systems.
• To construct equivalent integer-order models that preserve the original system's dynamics.
• To treat the fractional order as a variable for robust dynamic property capture.

Main Methods:

• Utilizing extended sparse regression to fit data with candidate functions.
• Employing cross-validation to select the most accurate and parsimonious equation.
• Treating the fractional order as a variable during the identification process.

Main Results:

• Identified optimal equations accurately represent fractional system dynamics.
• Equivalent models successfully capture dynamic behaviors across varying fractional orders.
• Identified systems exhibit stochastic P-bifurcation phenomena, similar to original fractional systems, without non-local terms.

Conclusions:

• The proposed method provides an effective way to identify fractional dynamic systems from data.
• Equivalent integer-order models can replicate complex dynamics, including P-bifurcation, without memory.
• This data-centric approach offers a new perspective on analyzing and modeling fractional systems.