Job offer for a PhD in Control
It is for a duration of 36months, in CentraleSupélec, Université Paris-Saclary, Gif-sur-Yvette, France
Contact: Jean Auriol (email@example.com), Riccardo Bonalli (firstname.lastname@example.org)
Deadline for application: May 10th
Thesis goal: Design methods for efficient and theoretically guaranteed control of a broad class of Stochastic differential equations (SDEs) coupled with Partial differen- tial equations (PDEs) systems. The proposed approaches will have to be constructive to obtain a semi-explicit design of the corresponding control laws, enabling performance-efficient numerical paradigms.
Investigate under which conditions the well-posedness of statistical linearization can be strength- ened, enabling general efficient and reliable numerical methods for the control of SDEs.
Investigate under which conditions the most recent methods for PDE–ODE can be extended to a broader class of systems, and in particular develop techniques which are as much independent as possible from any inherent regularizing property of the system (e.g., optimization methods).
Leverage statistical linearization to transform the SDE defining the SDE+PDE system of inter- est into a (constrained) well-posed Ordinnary Differential Equations (ODEs), and leverage the aforementioned improved methods for PDE–ODE systems to design efficient control strategies for the original SDE+PDE system.
Although the objective of the thesis consists of developing control methods which work in very general settings, we plan to showcase the efficiency of the proposed approaches through numerical simulations on specific examples (for instance, on DHCSs). Implementation on a real robotic system might be considered, which might result in an external collaboration with Stanford University.