Optimal control problems: analysis, approximation and applications (n. 2022238YY5)
Type
PRIN 2022, D.D. n. 104 del 2 febbraio 2022
CUP
C53D23002370006,
Principal Investigator
Giovanni Colombo (Universit
Other research units
UO1 - Elisabetta CARLINI - Universit
Duration
28/09/2023 - 28/02/2026
Description
The project joins together 3 research units working on control problems since many years, they include several researchers with different skills ranging from analysis of control problems with geometric control and dynamic programming techniques to numerical methods and applications. The main characteristic of this project is the mixture of theoretical and numerical methods for the solution of challenging control problems.
The goal is to introduce new techniques for some classical questions and to study new problems in control theory from the analytical and numerical point of view. The research program is organized into three work packages, namely:
WP1) Optimal control problems for systems driven by ordinary differential equations
WP2) Optimal control problems for systems driven by partial differential equations
WP3) Optimal control approach to machine learning
WP1 includes the analysis and approximation of optimal control problems for delay differential equations, problems with state constraints and control problems on networks as well as high order necessary conditions for non-smooth vector fields.
WP2 includes the analysis and approxim ation of optimal control problems for evolutive partial differential equations (e.g Navier-Stokes, Euler, Burgers..), delay partial differential equations as well as the control of some multi-agent systems.
WP3 is devoted to the mathem atical interpretation and modeling of some machine learning methods via control theory. This includes the analysis and approximation of Deep Neural Networks (DNN) and Reinforcement learning.
Activities
Organizzate una scuola (Gaeta, maggio 2024) e due convegni (Padova, settembre 2024; Roma, settembre 2025); a Padova 18 mesi di assegno di ricerca
