« Infinite-dimensional internal model regulators for finite-dimensional nonlinear systems »
Location: UCBL1 http://www.univ-lyon1.fr/
Lab: LAGEPP http://www.lagep.univ-lyon1.fr
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 . 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  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 . 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 . During the project, we aim also at developing new tools for the stabilization of interconnections of PDE and (nonlinear) ODEs  and at studying the finite dimensional realization of the proposed regulators for practical implementation purposes . The control problem of heat exchanger networks will be used as a pilot test for experimental validations of the proposed methodology .
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.
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
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] univ-lyon1.fr
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 [at] univ-lyon1.fr
 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.
 M. Bin, D. Astolfi and L. Marconi, About Robustness of Control Systems Embedding an Internal Model, IEEE Transactions on Automatic Control, March 2023.
 D. Astolfi, S. Marx, and N. van de Wouw, Repetitive control design based on forwarding for nonlinear minimum-phase systems, Automatica, vol. 129, 109671, July 2021.
 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.
 D. Astolfi, L. Praly and L. Marconi, Harmonic Internal Models for Structurally Robust Periodic Output Regulation, System & Control Letters, vol. 161, 105154, March 2022.
 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.