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. Mathew, James; Lefèvre, Philippe; Crevecoeur, Frédéric. Rapid changes in movement representations during human reaching could be preserved in memory for at least 850ms. In: eneuro, , p. ENEURO.0266-20.2020 (2020). doi:10.1523/eneuro.0266-20.2020 (Accepté/Sous presse). http://hdl.handle.net/2078.1/237547

2. Yuan, Xinru; Huang, Wen; Absil, Pierre-Antoine; Gallivan, Kyle A. Computing the matrix geometric mean: Riemannian versus Euclidean conditioning, implementation techniques, and a Riemannian BFGS method. In: Numerical Linear Algebra with Applications, Vol. 27, no.5, p. 2321 (2020). doi:10.1002/nla.2321. http://hdl.handle.net/2078.1/235049

3. Hendrickx, Julien. Julien M. Hendrickx [People in Control]. In: IEEE Control Systems Magazine, Vol. 40, no.4, p. 21-22 (2020). doi:10.1109/MCS.2020.2990512. http://hdl.handle.net/2078.1/235005

4. Van Hoorebeeck, Loïc; Absil, Pierre-Antoine; Papavasiliou, Anthony. Global Solution of Economic Dispatch with Valve Point Effects and Transmission Constraints. In: Electric Power Systems Research, Vol. 189, p. 106786 (2020). doi:10.1016/j.epsr.2020.106786. http://hdl.handle.net/2078.1/232186

5. De Klerk, Etienne; Glineur, François; Taylor, Adrien B. Worst-Case Convergence Analysis of Inexact Gradient and Newton Methods Through Semidefinite Programming Performance Estimation. In: SIAM Journal on Optimization, Vol. 30, no.3, p. 2053-2082 (2020). doi:10.1137/19m1281368. http://hdl.handle.net/2078.1/232178

6. Gutiérrez-Gómez, Leonardo; Vohryzek, Jakub; Chiêm, Benjamin; Baumann, Philipp S.; Conus, Philippe; Cuenod, Kim Do; Hagmann, Patric; Delvenne, Jean-Charles. Stable biomarker identification for predicting schizophrenia in the human connectome. In: NeuroImage: Clinical, Vol. 27, p. 102316 (2020). doi:10.1016/j.nicl.2020.102316. http://hdl.handle.net/2078.1/231262

7. White, Olivier; Gaveau, Jérémie; Bringoux, Lionel; Crevecoeur, Frédéric. The gravitational imprint on sensorimotor planning and control. In: Journal of Neurophysiology, (2020). doi:10.1152/jn.00381.2019 (Accepté/Sous presse). http://hdl.handle.net/2078.1/230746

8. Crevecoeur, Frédéric; Mathew, James; Bastin, Marie; Lefèvre, Philippe. Feedback Adaptation to Unpredictable Force Fields in 250 ms. In: eneuro, Vol. 7, no.2, p. ENEURO.0400-19.2020 (2020). doi:10.1523/eneuro.0400-19.2020. http://hdl.handle.net/2078.1/230744

9. Legat, Benoît; Tabuada, Paulo; Jungers, Raphaël M. Sum-of-Squares methods for controlled invariant sets with applications to model-predictive control. In: Nonlinear Analysis: Hybrid Systems, Vol. 36, p. 100858 (2020). doi:10.1016/j.nahs.2020.100858. http://hdl.handle.net/2078.1/229374

10. Gomez, Marco A.; Jungers, Raphaël M.; Michiels, Wim. On the m-dimensional Cayley–Hamilton theorem and its application to an algebraic decision problem inferred from the H2 norm analysis of delay systems. In: Automatica, Vol. 113, p. 108761 (2020). doi:10.1016/j.automatica.2019.108761. http://hdl.handle.net/2078.1/229373

Conference Papers

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

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

3. Dewez, Julien; Glineur, François. Lower bounds on the nonnegative rank using a nested polytopes formulation. http://hdl.handle.net/2078.1/229853

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

5. Farjadnia, Mahsa; Wang, Zheming; Jungers, Raphaël M.. Stability Analysis of Data Driven Complex Systems. http://hdl.handle.net/2078.1/232497

6. Jungers, Raphaël M.; Tabuada, Paulo. Non-local Linearization of Nonlinear Differential Equations via Polyflows. http://hdl.handle.net/2078.1/229380

7. Azfar, Umer; Catalano, Costanza; Charlier, Ludovic; Jungers, Raphaël M.. A Linear Bound on the K-Rendezvous Time for Primitive Sets of NZ Matrices. In: Developments in Language Theory : Lecture Notes in Computer Science, 2019, 9783030248857, p. 59-73. doi:10.1007/978-3-030-24886-4_4. http://hdl.handle.net/2078.1/229379

8. Athanasopoulos, Nikolaos; Jungers, Raphaël M.. Polyhedral Path-Complete Lyapunov Functions. In: 2019 IEEE 58th Conference on Decision and Control (CDC), IEEE, 2019, 9781728113982. doi:10.1109/cdc40024.2019.9029905. http://hdl.handle.net/2078.1/229377

9. Philippe, Matthew; Jungers, Raphaël M.. A complete characterization of the ordering of path-complete methods. In: Proceedings of the 22nd ACM International Conference on Hybrid Systems Computation and Control - HSCC '19, ACM Press, 2019, 9781450362825, p. 138-146. doi:10.1145/3302504.3311803. http://hdl.handle.net/2078.1/229376

10. Van Hoorebeeck, Loïc; Absil, Pierre-Antoine; Papavasiliou, Anthony. MILP-Based Algorithm for the Global Solution of Dynamic Economic Dispatch Problems with Valve-Point Effects. In: 2019 IEEE Power & Energy Society General Meeting (PESGM), IEEE, 2019, 9781728119816. doi:10.1109/pesgm40551.2019.8973631. http://hdl.handle.net/2078.1/226986