Thèse Commande de Systèmes Non Linéaires par Réseaux de Neurones Conception Certification et Applications à la Robotique Autonome H/F - Doctorat.Gouv.Fr

Établissement : Université Côte d'Azur École doctorale : STIC - Sciences et Technologies de l'Information et de la Communication Laboratoire de recherche : I3S - Informatique, Signaux et Systèmes de Sophia-Antipolis Direction de la thèse : Guillaume DUCARD ORCID 0000000274004915 Début de la thèse : 2026-11-01 Date limite de candidature : 2026-05-03T23:59:59 Les contrôleurs à base de réseaux de neurones (CRN) sont de plus en plus considérés comme une alternative prometteuse aux approches classiques de commande pour les systèmes non linéaires. En particulier, ils peuvent être entraînés hors ligne pour approximer des lois de commande coûteuses en calcul, telles que la commande prédictive basée sur un modèle (MPC), permettant ainsi une implémentation en temps réel sur des systèmes embarqués.

Malgré ces avantages, leur utilisation dans des applications critiques en termes de sécurité reste limitée. Le principal problème réside dans le fait que les garanties de stabilité, de robustesse et de respect des contraintes sont généralement perdues lors du processus d'apprentissage, ce qui rend leur certification difficile.

Ce projet doctoral vise à développer un cadre méthodologique pour la conception et la certification de contrôleurs à réseaux de neurones pour systèmes dynamiques non linéaires. L'approche proposée s'appuiera sur des outils d'analyse de stabilité basés sur les fonctions de Lyapunov et l'optimisation par sommes de carrés (SOS), afin de fournir des garanties formelles en boucle fermée, tout en réduisant le conservatisme des méthodes existantes.
Les applications viseront des systèmes dynamiques non linéaires, potentiellement instables, notamment en robotique autonome, incluant des véhicules aériens impliqués dans des missions de sécurité civile et de surveillance environnementale.
Neural-network controllers (NNCs) are increasingly considered a promising alternative to classical control approaches for nonlinear systems. In particular, they can be trained offline to approximate computationally expensive control laws such as Model Predictive Control (MPC), enabling real-time deployment on embedded systems.

Despite these advantages, their use in safety-critical applications remains limited. The main issue is that stability, robustness, and constraint satisfaction guarantees are generally lost during the learning process. As a result, neural-network controllers are difficult to certify and therefore rarely deployed in systems requiring high reliability.

Recent research has proposed several frameworks for the analysis and certification of neural-network-based control systems, including Lyapunov-based methods, mixed-integer programming, and Sum-of-Squares (SOS) optimization techniques. Within this context, SOS-based approaches provide a powerful mathematical framework for stability analysis, but their applicability to complex nonlinear and high-dimensional robotic systems remains limited.

This doctoral project builds on existing SOS-based methodologies developed within the research group and aims to extend them toward the certification of neural-network controllers applied to realistic nonlinear robotic systems. In particular, the focus will be on unstable and constrained dynamical systems such as autonomous aerial vehicles.

Applications will focus on nonlinear and potentially unstable dynamical systems, particularly in autonomous robotics, including aerial vehicles. The main objective is to develop methodologies enabling the synthesis of neural-network controllers with formal guarantees on:
- Closed-loop stability
- Robustness to uncertainties and disturbances
- Performance under constraints
The key scientific challenges are:
- Extending stability analysis tools to nonlinear systems with NN controllers in the loop
- Reducing the conservatism of existing certification methods
- Scaling methods to larger neural networks
- Integrating learning and certification within a unified framework
The proposed research follows a structured methodology combining control design, machine learning, and optimization-based certification tools.

First, a nonlinear dynamical system representative of autonomous robotic platforms will be modeled. A baseline stabilizing controller (e.g., Model Predictive Control or nonlinear control techniques) will be designed, ensuring stability, robustness, and constraint satisfaction.

Second, a neural-network controller will be trained offline to approximate the baseline controller. Particular attention will be given to selecting suitable network architectures that balance approximation accuracy and compatibility with formal verification methods.

Third, a certification framework will be developed or applied to assess closed-loop stability properties. This will rely on Lyapunov-based analysis and Sum-of-Squares (SOS) optimization, enabling the construction of stability certificates and the estimation of regions of attraction. Extensions to robust stability and scalability to larger networks will be investigated.

Finally, an iterative approach combining learning and certification will be explored, where the neural-network controller is progressively improved (e.g., using reinforcement learning) while enforcing stability constraints.

The proposed methods will be validated through numerical simulations, hardware-in-the-loop experiments, and real-world tests on autonomous robotic systems, including aerial platforms.

Please see the attached pdf of the research proposal for more details.

Le candidat devra être titulaire d'un M2 ou grade équivalent au moment du recrutement. Le candidat doit maîtriser : théorie du contrôle, du filtrage et d'estimation, intelligence artificielle, apprentissage machine, Matlab/Simulink, C/C++, Python, ROS, etc. Passion pour la recherche interdisciplinaire de la théorie à l'application. Excellent niveau d'anglais parlé et écrit.