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. It participates in various projects including the Inter-university Attraction Pole on Dynamical Systems, Control and Optimization (DYSCO).

Principal Investigators :

Pierre-Antoine AbsilVincent Blondel, Jean-Charles Delvenne, Yves Deville, Denis DochainFrançois Glineur, Julien Hendrickx, Raphaël Jungers, Philippe Lefèvre, Yurii Nesterov, Pierre Schaus, Paul Van Dooren, 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. Vandaele, Arnaud; Glineur, François; Gillis, Nicolas. Algorithms for positive semidefinite factorization. In: Computational Optimization and Applications, Vol. 71, no.1, p. 193-219 (2018). doi:10.1007/s10589-018-9998-x. http://hdl.handle.net/2078.1/201944

2. Dopico, Froilán M.; Lawrence, Piers W.; Pérez, Javier; Van Dooren, Paul. Block Kronecker linearizations of matrix polynomials and their backward errors. In: Numerische Mathematik, (2018). doi:10.1007/s00211-018-0969-z. http://hdl.handle.net/2078.1/200798

3. Dopico, Froilán M.; Pérez, Javier; Van Dooren, Paul. Structured backward error analysis of linearized structured polynomial eigenvalue problems. In: Mathematics of Computation, , p. 1 (2018). doi:10.1090/mcom/3360. http://hdl.handle.net/2078.1/200697

4. Taylor, Adrien B.; Hendrickx, Julien; Glineur, François. Exact Worst-Case Convergence Rates of the Proximal Gradient Method for Composite Convex Minimization. In: Journal of Optimization Theory and Applications, Vol. 178, p. 455-476 (2018). doi:10.1007/s10957-018-1298-1. http://hdl.handle.net/2078.1/198401

5. Birpoutsoukis, Georgios; Csurcsia, Péter Zoltán; Schoukens, Johan. Efficient multidimensional regularization for Volterra series estimation. In: Mechanical Systems and Signal Processing, Vol. 104, p. 896-914 (2018). doi:10.1016/j.ymssp.2017.10.007. http://hdl.handle.net/2078.1/195999

6. Huang, Wen; Absil, Pierre-Antoine; Gallivan, K. A. A Riemannian BFGS Method Without Differentiated Retraction for Nonconvex Optimization Problems. In: SIAM Journal on Optimization, Vol. 28, no.1, p. 470-495 (2018). doi:10.1137/17m1127582. http://hdl.handle.net/2078.1/195965

7. Shikhman, V.; Nesterov, Yurii; Ginsburgh, V. Power method tâtonnements for Cobb–Douglas economies. In: Journal of Mathematical Economics, Vol. 75, p. 84-92 (2018). doi:10.1016/j.jmateco.2017.12.010. http://hdl.handle.net/2078.1/195953

8. Lu, Haihao; Freund, Robert M.; Nesterov, Yurii. Relatively Smooth Convex Optimization by First-Order Methods, and Applications. In: SIAM Journal on Optimization, Vol. 28, no.1, p. 333-354 (2018). doi:10.1137/16m1099546. http://hdl.handle.net/2078.1/195950

9. Jungers, Raphaël M.; Kundu, Atreyee; Heemels, W.P.M.H. Observability and controllability analysis of linear systems subject to packet losses. In: IEEE Transactions on Automatic Control,. doi:10.1109/TAC.2017.2781374 (Accepté/Sous presse). http://hdl.handle.net/2078.1/194096

10. Necoara, Ion; Nesterov, Yurii; Glineur, François. Linear convergence of first order methods for non-strongly convex optimization. In: Mathematical Programming, (2018). doi:10.1007/s10107-018-1232-1. http://hdl.handle.net/2078.1/193956

Conference Papers

1. Lara Cisneros, Gerardo; Dochain, Denis. On-line estimation of the VFA concentration in anaerobic digestion processes based on a super-twisting observer. http://hdl.handle.net/2078.1/197274

2. Martin, Benoît; Glineur, François; De Rua, Philippe; De Jaeger, Emmanuel. Loss reduction in a windfarm participating in primary voltage control using an extension of the Convex DistFlow OPF. In: Proceedings of the 20th Power Systems Computation Conference, IEEE, 2018, 978-1-910963-10-4. doi:10.23919/PSCC.2018.8442758. http://hdl.handle.net/2078.1/195309

3. Romo Hernandez, Aaron; Dochain, Denis; Hudon, Nicholas; Ydstie, Birger Erik. A Non-equilibrium Approach to Model Flash Dynamics with Interface Transport. http://hdl.handle.net/2078.1/195026

4. Dilip, S.; Athanasopoulos, Nikolaos; Jungers, Raphaël M.. The impact of packet dropouts on the reachability energy. http://hdl.handle.net/2078.1/194094

5. Dzyga, Michalina; Ferens, Robert; Gusev, Vladimir; Szykula, Marek. Attainable Values of Reset Thresholds. In: Leibniz International Proceedings in Informatics (LIPIcs). Vol. 83, no.40, p. 1-14 (2017). Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik: Dagstuhl, Germany, 2017. doi:10.4230/LIPIcs.MFCS.2017.40. http://hdl.handle.net/2078.1/196224

6. Cláudio Gomes; Legat, Benoît; Jungers, Raphaël M.; Hans Vangheluwe. Stable Adaptive Co-simulation: A Switched Systems Approach. http://hdl.handle.net/2078.1/195570

7. Sketch, Sean M.; Simpson, Cole S.; Crevecoeur, Frédéric; Okamura, Allison M.. Simulating the impact of sensorimotor deficits on reaching performance. In: 2017 International Conference on Rehabilitation Robotics (ICORR), IEEE, 2017. doi:10.1109/icorr.2017.8009217. http://hdl.handle.net/2078.1/194812

8. Bhowmick, Ayan Kumar; GUEUNING, Martin; Delvenne, Jean-Charles; Lambiotte, Renaud; Mitra, Bivas. Temporal Pattern of (Re)tweets Reveal Cascade Migration. In: Proceedings of the 2017 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining 2017 - ASONAM '17, ACM Press, 2017, p. 483-488. doi:10.1145/3110025.3110084. http://hdl.handle.net/2078.1/194702

9. Gonze, François; Gusev, Vladimir; Gerencser, Balazs; Jungers, Raphaël M.; Volkov, Mikhail V.. On the Interplay Between Babai and Černý’s Conjectures. In: Developments in Language Theory : Lecture Notes in Computer Science, Springer International Publishing, 2017, 9783319628080, p. 185-197. doi:10.1007/978-3-319-62809-7_13. http://hdl.handle.net/2078.1/194138

10. Gonze, François; Simonetto, Andrea; Huens, Etienne; Boucquey, Jean; Jungers, Raphaël M.. Probabilistic Occupancy Counts and Flight Criticality Measures for ATM. http://hdl.handle.net/2078.1/194136