The topic is related to a running GACR project by Didier Henrion "Semidenite programming for polynomial optimal control problems". The project focuses on the application of semidenite programming for solving numerically nonconvex optimal control problems with polynomial data, with a special focus on problems coming from aerospace systems control. It relies upon a diverse mathematical background ranging from functional analysis (measure theory, moments, partial differential equations, PDE), optimization (linear matrix inequalities, LMI and semidenite programming, SDP), to algebraic geometry (positive multivariate polynomials).
The objective of the project is a better understanding of the use of semidenite programming relaxations in the context of semialgebraic nonconvex optimal control problems, with a focus on explicit and reproducible numerical experiments coming from aerospace benchmark problems. The role of the PhD student would be among others to produce a collection of benchmark examples coming from aircraft design problems, and to produce a software module for nonlinear dynamical systems analysis design, to be integrated into our existing Matlab package GloptiPoly 3.