Mathematical sciences
Host Department
Department of Mathematics
Webpage
https://dottorato.math.unipd.it/
Mathematical sciences
Research Topic A
Abstract of the proposed UNIPhD research project
During the research we will concentrate on the following problem: obtaining “higher order” necessary optimality conditions for optimal control problems with state constraints. Such conditions, which can be relevant to rule out of the optimality of a process when first-order conditions fail, are not investigated well enough. We plan to consider also non-conventional systems, such as systems with unbounded or impulsive controls, or with a nonsmooth dynamics. In view of the above, the higher order conditions must be expressed in terms of set-valued objects like set-valued Lie brackets.
Short bio
Denis holds a Master’s degree in Mathematics. He studied in Ural Federal University as a mathematician with in-depth study of Optimal Control Theory and Differential Equations, as well as Mathematical and Functional analyses. He graduated from university with honours, and his thesis was about developing a neural network framework with applications in object recognition theory. During his study, he participated in various mathematical events such as conferences and local seminars, which equipped him with the necessary knowledge for his future research. One of the biggest conferences where he made a presentation about Sub-Riemannian optimal control problem in the Martinet flat case took place in Sochi, at Sirius University.
