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. Berger, Guillaume; Jungers, Raphaël M. Formal Methods for Computing Hyperbolic Invariant Sets for Nonlinear Systems. In: IEEE Control Systems Letters, Vol. 4, no.1, p. 235-240 (2020). doi:10.1109/lcsys.2019.2923923. http://hdl.handle.net/2078.1/224895

2. Rocher, Luc; Hendrickx, Julien; de Montjoye, Yves-Alexandre. Estimating the success of re-identifications in incomplete datasets using generative models. In: Nature Communications, Vol. 10, no.1 (2019). doi:10.1038/s41467-019-10933-3. http://hdl.handle.net/2078.1/225321

3. Bastin, Georges; Coron, Jean-Michel; Hayat, Amaury; Shang, Peipei. Exponential boundary feedback stabilization of a shock steady state for the inviscid Burgers equation. In: Mathematical Models and Methods in Applied Sciences, Vol. 29, no.02, p. 271-316 (2019). doi:10.1142/s021820251950009x. http://hdl.handle.net/2078.1/225059

4. Abbate, Thomas; Fernandes de Sousa, Sofia; Dewasme, Laurent; Bastin, Georges; Vande Wouwer, Alain. Inference of dynamic macroscopic models of cell metabolism based on elementary flux modes analysis. In: Biochemical Engineering Journal, Vol. 151, p. 107325 (2019). doi:10.1016/j.bej.2019.107325. http://hdl.handle.net/2078.1/225044

5. Camps, Daan; Mastronardi, Nicola; Vandebril, Raf; Van Dooren, Paul. Swapping 2 × 2 blocks in the Schur and generalized Schur form. In: Journal of Computational and Applied Mathematics, (2019). doi:10.1016/j.cam.2019.05.022 (Accepté/Sous presse). http://hdl.handle.net/2078.1/224008

6. Dmytryshyn, Andrii; Johansson, Stefan; Kågström, Bo; Van Dooren, Paul. Geometry of Matrix Polynomial Spaces. In: Foundations of Computational Mathematics, , p. 1-28 (2019). doi:10.1007/s10208-019-09423-1. http://hdl.handle.net/2078.1/218206

7. Hendrickx, Julien; Gerencser, Balazs; Fidan, Baris. Trajectory convergence from coordinate-wise decrease of quadratic energy functions, and applications to platoons. In: IEEE Control Systems Letters, Vol. 4, no. 1, p. 151-156 (2019). doi:10.1109/LCSYS.2019.2922607. http://hdl.handle.net/2078.1/216598

8. Hastir, Anthony; Lamoline, François; Winkin, Joseph; Dochain, Denis. Analysis of the existence of equilibrium profiles in nonisothermal axial dispersion tubular reactors. In: IEEE Transactions on Automatic Control, (2019). doi:10.1109/TAC.2019.2921675 (Accepté/Sous presse). http://hdl.handle.net/2078.1/216392

9. Gevers, Michel; Bazanella, A. S.; Pimentel, G. A. Identifiability of dynamical networks with singular noise spectra. In: IEEE Transactions on Automatic Control, Vol. 64, no. 6, p. 2473-2479 (2019). doi:10.1109/TAC.2018.2866448. http://hdl.handle.net/2078.1/214054

10. Hendrickx, Julien; Gevers, Michel; Alexandre S. Bazanella. Identifiability of dynamical networks with partial node measurements. In: IEEE Transactions on Automatic Control, Vol. 64, no. 6, p. 2240-2253 (2019). doi:10.1109/TAC.2018.2867336. http://hdl.handle.net/2078.1/214049

Conference Papers

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

2. Pinto, Samuel C; Andersson, Sean B.; Hendrickx, Julien; Cassandras, Christos G.. Optimal Multi-Agent Persistent Monitoring of the Uncertain State of a Finite Set of Targets. In: IEEE Conference on Decision and Control, Including the Symposium on Adaptive Processes. Proceedings. p. 4280-4285 (2019). I E E E, 2019. http://hdl.handle.net/2078.1/225355

3. Hamaide, Valentin; Glineur, François. Predictive maintenance of a rotating condenser inside a synchrocyclotron. In: CEUR Workshop Proceedings. Vol. 2491, p. 1-12 (2019). http://hdl.handle.net/2078.1/225224

4. Hautecoeur, Cécile; Glineur, François. Accelerating Nonnegative Matrix Factorization Over Polynomial Signals With Faster Projections. In: 2019 IEEE 29th International Workshop on Machine Learning for Signal Processing (MLSP), IEEE, 2019, 9781728108247, p. 1-6. doi:10.1109/mlsp.2019.8918844. http://hdl.handle.net/2078.1/225222

5. Wang, Zheming; Jungers, Raphaël M.; Ong, Chong-Jin. Computation of the maximal invariant set of linear systems with quasi-smooth nonlinear constraints. In: 2019 18th European Control Conference (ECC), IEEE, 2019, 9783907144008, p. 3803-3808. doi:10.23919/ecc.2019.8796145. http://hdl.handle.net/2078.1/225017

6. Wang, Zheming; Jungers, Raphaël M.; Flandroy, Quentin; Herregods, Baptiste; Hernalsteens, Cedric. Finite-horizon covariance control of state-affine nonlinear systems with application to proton beamline calibration. In: 2019 18th European Control Conference (ECC), IEEE, 2019, 9783907144008, p. 3740-3745. doi:10.23919/ecc.2019.8796121. http://hdl.handle.net/2078.1/224976

7. Berger, Guillaume; Jungers, Raphaël M.. A Converse Lyapunov Theorem for p-dominant Switched Linear Systems. In: 2019 18th European Control Conference (ECC), IEEE, 2019, 9783907144008, p. 1263-1268. doi:10.23919/ecc.2019.8795923. http://hdl.handle.net/2078.1/224901

8. Olikier, Guillaume; Absil, Pierre-Antoine; De Lathauwer, Lieven. Variable Projection Applied to Block Term Decomposition of Higher-Order Tensors. In: Latent Variable Analysis and Signal Separation : Lecture Notes in Computer Science, Springer International Publishing, 2018, 9783319937632, p. 139-148. doi:10.1007/978-3-319-93764-9_14. http://hdl.handle.net/2078.1/206952

9. Renard, Emilie; Gallivan, Kyle A.; Absil, Pierre-Antoine. A Grassmannian Minimum Enclosing Ball Approach for Common Subspace Extraction. In: Latent Variable Analysis and Signal Separation : Lecture Notes in Computer Science, Springer International Publishing, 2018, 9783319937632, p. 69-78. doi:10.1007/978-3-319-93764-9_7. http://hdl.handle.net/2078.1/206910

10. Dong, Shuyu; Absil, Pierre-Antoine; Gallivan, Kyle. Graph learning for regularized low-rank matrix completion. In: MTNS 2018. p. 460-467 (2018). http://hdl.handle.net/2078.1/201674