Dynamical Systems, Control and Optimization

Space Greenhouse

Picture : schematic view of the space greenhouse

The Dynamical Systems, Control and Optimization group gathers about a dozen professors and over 30 PhD students and postdoctoral researchers.

Principal Investigators :

Pierre-Antoine AbsilVincent Blondel, Frédéric Crevecoeur, Jean-Charles Delvenne, Yves Deville, Denis DochainFrançois Glineur, Julien Hendrickx, Raphaël Jungers, Philippe Lefèvre, Yurii Nesterov, Pierre Schaus, Vincent Wertz

Research Areas :

Identification of dynamical systems is one of the first steps in the study of dynamical systems, since it addresses the issue of finding an appropriate model for its input/output behavior. Much of our work on identification has focused on understanding the connections between, identifiability, informative experiments, the information matrix and the minimization of a prediction error criterion.

Several new multi-agent models have been proposed and studied with behavior reminiscent of the partial entrainment behavior of the Kuramoto-Sakaguchi model, but with a greater potential for analysis and with applications to systems not related to coupled oscillators. The main emphasis on these dynamic models is to analyze the asymptotic clustering behavior. The analysis of such models is relevant in the study of opinion formation, interconnected water basins, platoon formation in cycling races, and the minimum cost flow problem.

We study fundamental issues in modeling, control design and stability analysis of physical networks described by hyperbolic systems of conservation laws and by distributed parameter systems modeling e.g. tubular reactors. We also study problems related to optimal prediction of nonlinear systems, such as the flow in channels (modeled by Saint-Venant equations), the modeling of the water level in water basins in order to prevent flooding and the prediction and control of traffic jams.

Optimization techniques play a fundamental role in the area of dynamical systems and they are being developed and analyzed at several levels, depending on the type of variables one wishes to optimize. Variables can be discrete (as in graph theoretic problems) or continuous (as in parametric optimization), but can also be infinite dimensional (as in optimal control over function spaces) and constrained (as in optimization on manifolds or on cones). The group has activities in each of these areas and also develops special purpose numerical techniques for dealing efficiently with such problems.

The activities here include microbial ecology and the modeling of wastewater treatment, including applications to various biological wastewater systems. We developed population balance models covering a large spectrum of applications in the industry of polymer production, crystallization, biotechnology or any process in which the size distribution of particles is essential for process quality. We also study the design and application of observers converging in finite time for a class of fed-batch processes.

We combine theoretical and experimental approaches to investigate the neural control of movement and its interactions with our environment. The mathematical models that are developed are based on experimental results from both normal and pathological subjects (clinical studies) and focus on the interaction between different types of eye movements and on eye/hand coordination. Our main research objective is to gain further insight into the nature and characteristics of high-level perceptual and motor representations in the human brain. 

Most recent publications

Below are listed the 10 most recent journal articles and conference papers produced in this research area. You also can access all publications by following this link : see all publications.

Journal Articles

1. Dewez, Julien; Gillis, Nicolas; Glineur, François. A geometric lower bound on the extension complexity of polytopes based on the f-vector. In: Discrete Applied Mathematics, (2021). doi:10.1016/j.dam.2020.09.028 (Accepté/Sous presse). http://hdl.handle.net/2078.1/243156

2. Bastin, Georges; Coron, Jean-Michel; Hayat, Amaury. Input-to-State Stability in sup norms for hyperbolic systems with boundary disturbances. In: Nonlinear Analysis, (2021). (Accepté/Sous presse). http://hdl.handle.net/2078.1/243079

3. Bastin, Georges; Coron, Jean-Michel; Hayat, Amaury. Feedforward boundary control of 2×2 nonlinear hyperbolic systems with application to Saint-Venant equations. In: European Journal of Control, Vol. 57, p. 41-53 (2021). doi:10.1016/j.ejcon.2020.11.002. http://hdl.handle.net/2078.1/243075

4. Mehrmann, Volker; Van Dooren, Paul. Structured Backward Errors for Eigenvalues of Linear Port-Hamiltonian Descriptor Systems. In: SIAM Journal on Matrix Analysis and Applications, Vol. 42, no.1, p. 1-16 (2021). doi:10.1137/20m1344184. http://hdl.handle.net/2078.1/242981

5. Danion, Frederic R.; Mathew, James; Gouirand, Niels; Brenner, Eli. More precise tracking of horizontal than vertical target motion with both the eyes and hand. In: Cortex, Vol. 134, p. 30-42 (2021). doi:10.1016/j.cortex.2020.10.001. http://hdl.handle.net/2078.1/241401

6. Gueuning, Martin; Cheng, Sibo; Lambiotte, Renaud; Delvenne, Jean-Charles. Rock–paper–scissors dynamics from random walks on temporal multiplex networks. In: Journal of Complex Networks, Vol. 8, no.2 (2019). doi:10.1093/comnet/cnz027. http://hdl.handle.net/2078.1/243512

7. Falasco, Gianmaria; Esposito, Massimiliano; Delvenne, Jean-Charles. Unifying thermodynamic uncertainty relations. In: New Journal of Physics, Vol. 22, no.5, p. 053046 (2020). doi:10.1088/1367-2630/ab8679. http://hdl.handle.net/2078.1/243510

8. Freitas, Nahuel; Delvenne, Jean-Charles; Esposito, Massimiliano. Stochastic and Quantum Thermodynamics of Driven RLC Networks. In: Physical Review X, Vol. 10, no.3 (2020). doi:10.1103/physrevx.10.031005. http://hdl.handle.net/2078.1/243508

9. Mehrmann, V; Van Dooren, Paul. Optimal robustness of passive discrete-time systems. In: IMA Journal of Mathematical Control and Information, Vol. 37, no.4, p. 1248-1269 (2020). doi:10.1093/imamci/dnaa013. http://hdl.handle.net/2078.1/242978

10. Mehrmann, Volker; Van Dooren, Paul. Optimal Robustness of Port-Hamiltonian Systems. In: SIAM Journal on Matrix Analysis and Applications, Vol. 41, no.1, p. 134-151 (2020). doi:10.1137/19m1259092. http://hdl.handle.net/2078.1/242971

Conference Papers

1. Crevecoeur, Frédéric; Mathew, James; Lefèvre, Philippe. Force cues flexibly separate motor memories in human reaching adaptation. 2021 xxx. http://hdl.handle.net/2078.1/242195

2. Debauche, Virginie; Jungers, Raphaël M.. On Path-Complete Lyapunov Functions : comparison between a graph and its expansion. 2020 xxx. http://hdl.handle.net/2078.1/242844

3. Shi, Mingming. Resilient asynchronous rendezvous of second-order agents under communication noise. 2020 xxx. http://hdl.handle.net/2078.1/238535

4. Shi,Ming; Feng,Shuai; Ishii,Hideaki. Quantized State Feedback Stabilization of Nonlinear Systems Under DoS. 2020 xxx. http://hdl.handle.net/2078.1/238534

5. Ramseier, Aude; Banaï, Myriam; Ducarme, Delphine; Wertz, Vincent. Évaluer à distance, dans l’urgence, un cours de dynamique de groupe. 2020 xxx. http://hdl.handle.net/2078.1/237045

6. Dewez, Julien; Glineur, François. Lower bounds on the nonnegative rank using a nested polytopes formulation. In: ESANN2020, 28th European Symposium on Artificial Neural Networks - Computational Intelligence and Machine Learning, 2020, 978-2-87587-073-5 xxx. http://hdl.handle.net/2078.1/229853

7. Hendrickx, Julien; Olshevsky, Alex; Saligrama, venkatesh. MinimaxRank-1Factorization. 2020 xxx. http://hdl.handle.net/2078.1/225595

8. Mathew, James; Bastin, M; Lefèvre, Philippe; Crevecoeur, Frédéric. Correlates of online changes in movement representations in 240ms. 2019 xxx. http://hdl.handle.net/2078.1/241745

9. Danion, Frederic R; Mathew, James; Gouirand, Niels; Brenner, Eli. Separate contribution of eye movements to hand tracking and its adaptation to visuomotor rotation. 2019 xxx. http://hdl.handle.net/2078.1/241744

10. Lefèvre, Philippe; Mathew, James; Crevecoeur, Frédéric. Online changes in movement representations could be preserved in memory for at least 500ms. 2019 xxx. http://hdl.handle.net/2078.1/241743