PhD "Nonlinear output Regulation"

Type de recrutement
Fin de l'affichage

Ph.D. Position:

« Infinite-dimensional internal model regulators for finite-dimensional nonlinear systems »


Location: UCBL1



Main advisor: Daniele Astolfi (CNRS - LAGEPP)


Scientific Domain: Control theory, mathematics, dynamical system, engineering.


Objectives, scientific challenges and expected original contributions: The problem of rejecting constant disturbances while following references is a central issue in control theory. It is also known as robust output regulation problem, and it arises in most control feedback applications, from engineering, to neuroscience [1]. For controlled plants described by linear dynamics, such a problem has been solved in the 70’s by means of the celebrated internal-model principle [1] claiming that asymptotic output regulation can be achieved robustly with respect to parametric uncertainties only if the regulator replicates a suitable copy of the dynamical model generating the disturbances or references [5, Section 3]. For constant signals, this consists in using an integral action in the feedback-loop. In the context of nonlinear systems, no general theory is available, although research is still active in this domain [2]. The objective of this project is to study the robust output regulation problem of finite-dimensional nonlinear systems by means of infinite-dimensional internal model controllers, providing an exhaustive solution to such a fundamental problem that has been open for more than 50 years. Following the celebrated internal model principle, we aim at developing the theory of infinite-dimensional regulators by means of conservative and dissipative operators, following the preliminary ideas developed in [3]. During the project, we aim also at developing new tools for the stabilization of interconnections of PDE and (nonlinear) ODEs [4] and at studying the finite dimensional realization of the proposed regulators for practical implementation purposes [5]. The control problem of heat exchanger networks will be used as a pilot test for experimental validations of the proposed methodology [6].


Length and remuneration of the Ph.D.: 36 months with a salary of around 1500€ net per month, to be started between September 2023 and November 2023. The salary can be increased by around 200€ net per month by teaching (bachelor/master’s degree level) around 60 hours per year. For teaching, the French language is usually needed.


Candidate profile: 

We are looking for self-motivated team-player candidates that match the following profile:

 - A Master’s degree in Control Systems, Mathematics, Mechatronics or Dynamic Systems-related

disciplines with excellent grades;

- Excellent academic records, solid mathematical background, excellent knowledge in dynamic systems; good computer programming skills are a plus but not mandatory.

- Excellent oral and written communication skills;

- English language mastery (writing and presenting) is mandatory.

- French language is a plus, but not mandatory


Eligibility criteria:

Applicants must fulfill the following eligibility criteria:

- At the time of the application, applicants must be in possession or finalizing their Master’s degree or equivalent/postgraduate degree;

- At the time of recruitment, applicants must be in possession of their Master’s degree or equivalent/postgraduate degree which would formally entitle them to embark on a doctorate.



All applications should be compressed (.zip, 5MB max.) and submitted by email to the addresses


daniele.astolfi [at]


with the title


PhD application 2023 (project Alligator): name surname




- Cover letter including a statement of purpose and previous experiences;

- Detailed curriculum vitae;

- Course grades transcripts;

- A scientific writing sample (Master thesis, seminar paper, or equivalent);

- Contact information of two references.


For more information concerning this position, please contact:


Daniele Astolfi

daniele.astolfi [at]


References :

[1] M. Bin, J. Huang, A. Isidori, L. Marconi, M. Mischiati, E. Sontag, Internal Models in Control, Bioengineering, and Neuroscience, Annual Review of Control, Robotics, and Autonomous Systems vol. 5, pp. 55-79.

[2] M. Bin, D. Astolfi and L. Marconi, About Robustness of Control Systems Embedding an Internal Model, IEEE Transactions on Automatic Control, March 2023.

[3] D. Astolfi,  S. Marx,  and N. van de Wouw, Repetitive control design based on forwarding for nonlinear minimum-phase systemsAutomatica, vol. 129, 109671, July 2021.

[4] S. Marx, L. Brivadis and D. Astolfi, Forwarding techniques for the global stabilization of dissipative infinite-dimensional systems coupled with an ODE, Mathematics of Control, Signals, and Systems, vol. 33 (12), pp. 755-774, December 2021. 

[5] D. Astolfi, L. Praly and L. Marconi, Harmonic Internal Models for Structurally Robust Periodic Output Regulation, System & Control Letters, vol. 161, 105154, March 2022.

[6] B. Zitte, B. Hamroun, D. Astolfi and F. Couenne, Robust Control of a Class of Bilinear Systems by Forwarding: Application to Counter Current Heat Exchanger, 21st IFAC 2020 World Congress, Berlin, Germany, July 2020.