# Fractional Calculus in Engineering Sciences: Modeling, System Identification and Control of living and autonomous systems

Stéphane Victor

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Stéphane Victor. Fractional Calculus in Engineering Sciences: Modeling, System Identification and Control of living and autonomous systems. 2025. hal-05446469

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Submitted on 7 Jan 2026

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# Fractional Calculus in Engineering Sciences: Modeling, System Identification and Control of living and autonomous systems

Stéphane VICTOR, Associate Professor Université de Bordeaux, France

## Abstract

The research theme of the CRONE team (Command - Robotics - Non-Integer Orders) of the Automatic Group of the IMS laboratory - UMR 5218 CNRS, focuses on the theme of "Non-integer derivative systems". This research theme was initiated in 1975 by Alain Oustaloup and falls under the **non-integer derivation** as operator and modeling tool, its synthesis extended to the body of complexes as well as its applications in engineering science. More specifically, the research axes of the CRONE team focus on the application of non-integer derivation in system theory, in automatic control through modeling by non-integer model, identification by non-integer model and robust control (abbreviation for Non-Integer Order Robust Command) and finally, in robotics through trajectory planning, vibration isolation and setpoint and control generation. The non-integer derivation operator (real or complex) has many assets, namely the **property of long memory**, which allows it to well describe diffusion phenomena (thermal, electrochemical, biological,...) as well as the **property of parametric compactness** which thus constitutes the mathematical tool par excellence to model with few parameters, a large number of diffusion phenomena that fall under engineering sciences as well as the biological sciences. In addition, the non-integer derivation operator **generalizes** the ``integer'' derivation operators and is a very effective synthesis tool in the field of Automatic control (in identification, robust control, trajectory planning, reference and control generation, etc.). The CRONE team is committed to developing decisive theoretical foundations, capitalizing and disseminating them through the development of the Crone toolbox, then, for the sake of application, to concretize them through technological transfers that are part of a real enhancement of upstream and partnership research.

## Biography and research work

In 2006, Stéphane Victor completed his third year of ENSEIRB engineering school on exchange at the Ecole Poytechnique Montreal (Canada) in parallel with the AM2AS (Automatic control) Research Master at the University of Bordeaux.
His research internship at the Department of Mechanical Engineering of the Ecole Polytechnique focused on linear systems with delay on control and state and gave me the attraction for fundamental research in automatic control.

Stéphane Victor did his doctoral thesis at IMS/Univ. Bordeaux laboratory, on system identification by non-integer model and robust trajectory tracking by flatness, defended in November 2010.

The following year, in 2011, he was recruited as associate professor at the University of Bordeaux within the same research team.

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His research activities revolve around the non-integer derivative as an operator and modeling tool, but also as a tool in control and trajectory planning. More specifically, he is interested in:

- fundamental aspects related to **system theory** with non-integer derivatives, in particular the extension of flatness principles

- methodological aspects related to **trajectory planning** (by multi-criteria optimization of trajectory (2D and 3D) to establish the generation of instructions and commands, for obstacle avoidance and trajectory replanning)
- methodological aspects related to **modeling of non-integer systems** (modeling of heat transfers in the lungs, modeling of the terrestrial climate system and modeling of wind turbulence for antennas)

- methodological aspects related to the **identification of dynamical systems** by non-integer model (non-commensurate, closed-loop, multivariate, real-time systems)

- application aspects in the field of **autonomous vehicle** (2D for the car with the PSA Group (Stellantis) in particular and 3D for the drone with the Synum cluster), in the **biological** field (heat transfer modeling), in the **climatic** field (modeling of the Earth's climate system and wind turbulence modeling with Safran Data System), in the field **aeronautics** (identification and control of a turbofan developed by Price Induction, now acquired by Safran)

- and capitalizing on know-how through the development of the object-oriented version of the **CRONE toolbox/Matlab®** dedicated to modeling and identifying systems.

This talk is devoted to a synthesis of my contributions around fractional calculus both theoretical and applicative.