Interactions of Control, Partial Differential Equations and Numerics – ICON

This project aims at making a breakthrough contribution in the broad area of Control of Partial Differential Equations (PDE) and their numerical approximation methods by addressing some key issues that remain badly understood or unsolved and which appear systematically in all real-life applications.
To this end, we pursue three objectives: to contribute with new key theoretical methods and results; to develop the corresponding numerical tools and new computational software, thereby bridging the gap to applications.
The theory of PDEs, together with numerical approximation and simulation methods and control theory, have evolved significantly in the last decades, in a cross-fertilization process to address the challenging demands of industrial and cross-disciplinary applications such as, for instance, the management of natural resources, pollution, meteorology, aeronautics, oil industry, biomedicine, human and animal collective behaviour, etc. However, despite these efforts some of the key issues still remain unsolved, either because of a lack of sufficient analytical understanding, or due to the absence of efficient numerical solvers.
This project identifies and focuses on six key topics that play a central role but which are still poorly understood: control of parameter dependent problems; long time horizon control; control under constraints; inversion of time-irreversible models; memory models and hybrid PDE/ODE models, and finite versus infinite-dimensional dynamical systems.
These topics cannot be handled by simply superposing the state of the art in the various disciplines, due to the unexpected interactive phenomena that may emerge, for instance, when dealing with limit processes from finite to infinite-dimensional dynamics. The coordinated and focused effort that we aim at developing is timely and much needed in order to solve these issues and bridge the gap from modelling to control, computer simulations and applications.
The Laboratoire Jacques Louis Lions of the Université Pierre et Marie Curie in Paris (LJLL-UPMC) is, possibly, the best institution in the world to develop this research agenda in collaboration with top scientists in the meeting point of the three domains in which the project focuses. The candidate will bring to the host institution a multidisciplinary perspective generating a new dynamics oriented to the numerics of control and its applications that will reinforce and renovate the expertise of the Laboratory in this key area.
The development of this project will allow the candidate not only to work in tight collaboration with the members of the LJLL-UPMC, but also with the other teams of the Ile-de-France region and France, in general, with whom he has been actively cooperating during over twenty-five years. This will also allow the applicant to get further involved in some international on-going projects in which the host team at LJLL-UPMC is taking part.
The integration of the PI in the LJLL-UPMC will also facilitate his involvement in teaching and dissemination activities addressed, respectively, to master and PhD students and the large public.