MASTER INTERNSHIP PROPOSAL

Master internship proposal

Decentralized flatness-based control for multi-agent systems

Subject: Investigation of flatness-based control of linear and nonlinear interconnected systems

Student profile: master student (bac+5) on control systems or mathematics. No previous experience

in control for power systems is required.

Duration: stage of 5-6 months, possibly starting February-March 2027.

Salary: 500-600 €, according to the working days of the month. Public transportation reimbursement.

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 [email protected])

————– Florentina Nicolau, l2s.centralesupelec.fr/u/nicolau-florentina/

————– (email [email protected])

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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).

In the context of power systems, current multi-agent flatness-based control strategies often concentrate

the global energy regulation burden on the master unit in a master-slave configuration, where the remain-

ing units act as dependent current sources. This asymmetry may lead to excessive transient current peaks

and a higher risk of controller saturation in case of model mismatches or unmodeled energy dissipation. To

overcome these limitations, we recently proposed a cooperative flatness-based control. As a consequence,

instead of relying on a single regulating unit, the proposed strategy distributes the regulation effort across

a network of cooperative agents. However, the proposed approach is a centralized one. Therefore, one of

the main goals of the internship is to generalize that method to a decentralized approach.

Desired Steps

• Literature investigation;
• Investigation of theoretical conditions and development of optimal solutions;
• Test on simulations.

Desired experience

• Knowledge of nonlinear control techniques;
• 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

[email protected] and [email protected] with object [stage Flat-

ness]

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.