Organizers: Frédéric Bonnans Place: École Polytechnique
July 06, 2015 (salle de conférence, CMAP)
14:00 Felix Henneke (TU Munich, Germany)
Title: Sparse control of bilinear quantum systems Abstract: Optimal control theory has proven to be a useful tool in controlling quantum systems. However, standard optimal control approaches lead to controls that are difficult to interpret and implement in experiments. We propose an optimal control framework to generate control fields with a very simple time-frequency structure. We achieve this by controlling a time-frequency representation of the field rather than the field itself, and by using cost functionals in the time-frequency plane that enhance sparsity in frequencies and smoothness in time. Mathematically this is realized by working in a space of function-valued measures, resulting in a non-smooth and non-convex optimization problem. In this talk I will give an outline of the proposed control framework, will discuss the structure of optimal controls and present numerical results for an example from molecular control.
June 29, 2015 (salle de conférence, CMAP)
11:00 Valeriya Naumova (Simula Research Laboratory AS, Norway)
Title: Learning Theory Approach to the Adaptive Regularization with Case
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April 23, 2015
14:00 Maria Soledad Aronna (IMPA, Brazil)
Title: Global stabilizing feedback law for a problem of biological control of mosquito-borne diseases Abstract: The control of the spread of dengue fever by introduction of the intracellular parasitic bacterium Wolbachia in populations of the vector Aedes aegypti, is presently one of the most promising tools for eliminating dengue, in the absence of an efficient vaccine. The success of this operation requires locally careful planning to determine the adequate number of mosquitoes carrying the Wolbachia parasite that need to be introduced into the natural population. The latter are expected to eventually replace the Wolbachia-free population and guarantee permanent protection against the transmission of dengue to human. In this paper, we propose and analyze a model describing the fundamental aspects of the competition between mosquitoes carrying Wolbachia and mosquitoes free of the parasite. We then introduce a simple feedback control law to synthesize an introduction protocol, and prove that the population is guaranteed to converge to a stable equilibrium where the totality of mosquitoes carry Wolbachia. The techniques are based on the theory of monotone control systems, as developed after Angeli and Sontag. Due to bistability, the considered input-output system has multivalued static characteristics, but the existing results are unable to prove almost-global stabilization, and ad hoc analysis has to be conducted.
15:15 Francisco Silva (Université de Limoges)
Title: A variational approach to second order mean field games with density constraints: The stationary case. Abstract: In this talk we consider second order stationary Mean Field Game systems under density constraints on a bounded domain $\Omega \subset \R^d$. We show the existence of weak solutions for power-like Hamiltonians with arbitrary order of growth. Our strategy is a variational one, i.e. we obtain the Mean Field Game system as the optimality condition of a convex optimization problem, which has a solution. This is a joint work with A. Richárd Mészáros (Université d'Orsay).
March 30, 2015 (salle de conférence, CPHT)
14:00 Jochen Garcke (University of Bonn, Germany)
Title: An Adaptive Sparse Grid semi-Lagrangian scheme for first-order Hamilton-Jacobi Bellman equations Abstract: We start with an introduction on sparse grids for high-dimensional function approximation. Following that, we propose a semi-Lagrangian scheme using a spatially adaptive sparse grid to deal with non-linear time-dependent Hamilton-Jacobi Bellman equations. We focus in particular on front propagation models in higher dimensions which are related to control problems. We test the numerical efficiency of the method on several benchmark problems up to space dimension d=8, and give evidence of convergence towards the exact viscosity solution. Finally, we investigate how the adaptive sparse grid scheme can be used in the planning stage of model-based reinforcement learning approach.
15:15 Sihem Tebbani (Dept. Automatique, CentraleSupelec)
Title: Robustification de l’estimation à horizon glissant pour des systèmes incertains : application aux bioprocédés Abstract: l’estimateur à horizon glissant (MHE) permet de reconstruire les états du système en temps réel. Il consiste à résoudre, en temps réel, un problème d’optimisation de type moindre carrés non linéaires. Dans le cas de systèmes incertains, le MHE peut présenter des erreurs d’estimation. Pour améliorer sa robustesse vis-à-vis des erreurs de modélisation, le problème d’optimisation est remplacé par un problème de type minmax, dont la résolution induit un temps de calcul important. Une nouvelle formulation est proposée dans cette présentation qui permet de robustifier l’estimation du MHE, tout en réduisant le temps de calcul par rapport à la résolution du problème minmax. Les performances de l’approche proposée sera illustrée en simulation dans le cas de bioréacteurs pour l’estimation de la concentration de biomasse.
March 16, 2015 (salle de conférence, CMAP)
14:00 Martin Gubisch (Konstanz University, Germany)
Title: POD Model Reduction for Optimal Control Problems Abstract: Solving an optimal control problem governed by a partial differential equation numerically usually requires to solve pdes of similar form several times. If standard methods such as finite differences or finite elements are used, an accurate discretization results in large linear systems. To decrease the number of unknowns, different model reduction techniques can be applied. The idea of Proper Orthogonal Decomposition (POD) is to construct a small, problem-specific Galerkin basis. Unfortunatelly, the initially given information often is not sufficient to find such a basis immediatelly; instead, the dynamics of the optimal pde solution are required. Hence, efficient updating techniques are required to achieve good approximations. The talk will give an introduction into POD model reduction and demonstrate its procedure at the example of state-constraint optimal control of a heat flux.