Nonlinear differential equations and stochastic models

Mathematical sciences


Host Department
Department of Mathematics



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

My name is Denis, I’m a master of mathematics. I 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. I’ve graduated from university with honours, and my thesis was about developing a neural network framework with applications in object recognition theory. During my study I’ve participated in various mathematical events such as conferences and local seminars which equipped me with necessary knowledge for my future research. One of the biggest conferences where I made a presentation about Sub-Riemannian optimal control problem in Martinet flat case took place in Sochi Sirius University.

Topic assigned to
Denis Shishmintsev


Project documents