Master internship proposal
Flatness-based control for multi-agent systems
Subject: Investigation of flatness of linear and nonlinear interconnected systems
Student profile: master student (bac+5), possibly with experience in control for power systems.
Duration: stage of 5-6 months, possibly starting February-March 2025.
Salary: 500-600 €, according to the working days of the month.
Work place: L2S, CentraleSupélec, 3, rue Joliot Curie, 91190 Gif-sur-Yvette, France.
Keywords: nonlinear control, flatness, multi-agent systems, simulations.
Advisor: Alessio Iovine, l2s.centralesupelec.fr/u/iovine-alessio/
————– (email alessio.iovine@centralesupelec.fr)
————– Florentina Nicolau, www.quartz-lab.fr/NICOLAU-Florentina?lang=en
————– (email florentina.nicolau@ensea.fr)
Internship description
Systems consisting of the interconnection of a certain number of subsystems are ubiquitous in emerg-
ing technologies, especially when nonlinear dynamics are taken into account. From power grids, fleets
of connected autonomous vehicles or drones, natural processes in biology and genetics, to online social
networks, they are all characterized by their complexity. When considering interconnected systems as a
whole, the interconnection plays an essential role in the control applications and call upon the develop-
ment of novel adapted tools for control design. An important question is: when suitable properties are
ensured for each subsystem, does the interconnected system share the same properties? In other words,
are these properties preserved by the interconnection?
A property that is very useful in applications (for instance, for trajectory tracking and trajectory gener-
ation) is that of differential flatness (that can be seen as a notion generalizing controllability for nonlinear
systems). Although differential flatness (simply, flatness) has received a lot of attention because of its
important applications, the problem of giving necessary and sufficient verifiable conditions in order to
check whether a system is flat remains widely open. In this internship, we target to characterize flatness
for some classes of multi-agent interconnected systems taking into account both the (controllable) several
agents and the (uncontrolled) interconnection variables. The classes of interconnected systems that will
be considered cover a large set of electrical systems and related controllers. From the point of view of
the application to power systems, we target to study and show how flatness for the global multi-agent
system can be a powerful tool to select desired trajectories (for instance, with the aim of stabilization)
while allowing for a selection of desired characteristics of the control inputs (for example, the capability
to share the control effort among the agents, which is a possibility of interest for electrical systems as of
current use).
Desired steps:
1. Literature investigation;
2. Investigation of theoretical conditions and development of optimal solutions;
3. Test on simple cases with toy-models;
4. Final implementation on realistic power systems’ models.
Desired experience
(a) Knowledge of nonlinear control techniques;
(b) MATLAB/Python.
References
[1] M. Fliess, J. Lévine, P. Martin, and P. Rouchon, (1995). Flatness and defect of non-linear systems:
introductory theory and examples. Internat. J. Control, 61(6), 1327–1361.
https://doi.org/10.1080/00207179508921959
[2] F. Nicolau, A. Iovine, « Flatness of interconnected linear systems and applications to electrical systems »,
published in IFAC COSY2022, IFAC-PapersOnLine, Volume 55, Issue 40, 2022, Pages 241-246, ISSN 2405-
8963. https://hal.archives-ouvertes.fr/hal-03771607/document
[3] S. Messaoudi, F. Nicolau, M. Ghanes, L. Sbita and J.P. Barbot Flatness-Based Control Strategy for n Par-
allel Connected Boost Choppers and n Sources with Differing Characteristics, IEEE Control Systems Letters,
vol. 7, pp. 3084-3089, 2023.
https://doi.org/10.1109/LCSYS.2023.3292038, https://hal.science/hal-04463931
[4] M. Laaziz, F. Nicolau, M. Ghanes, J.P. Barbot, and N. Machkour, Active fault-tolerant flatness-based
control for a three-phase grid connected inverter with LCL filters, European Journal of Control, 101331,
ISSN 0947-3580, 2025.
https://doi.org/10.1016/j.ejcon.2025.101331
Contacts
Send a CV, a motivation letter, transcripts of academic records and names of possible references to
alessio.iovine@centralesupelec.fr and florentina.nicolau@ensea.fr with object [stage Flatness]
The position is available immediately and applications will be accepted until this position is filled. A
National Security clearance is needed, and it can require approximately 2 months
