Ph.D. Thesis (2013-2016)

Numerical methods for hybrid control and chance-constrained optimization problems

This thesis is devoted to the analysis of numerical methods in the field of optimal control, and it is composed of two parts. The first part is dedicated to new results on the subject of numerical methods for the optimal control of hybrid systems, controlled by measurable functions and discontinuous jumps in the state variable simultaneously. The second part focuses on a particular application of trajectory optimization problems for space launchers. Here we use some nonlinear optimization methods combined with non-parametric statistics techniques. This kind of problems belongs to the family of stochastic optimization problems and it features the minimization of a cost function in the presence of a constraint which needs to be satisfied within a desired probability threshold.

This work is the result of the collaboration between ENSTA Paris and Airbus Safran Launchers. It is partially supported by the EU under the 7th Framework Programme Marie Curie Initial Training Network ``FP7-PEOPLE-2010-ITN'', SADCO project, GA number 264735-SADCO; and by iCODE Institute project funded by the IDEX Paris-Saclay, ANR-11-IDEX-0003-02.

Stage (September-November 2014)

Three-month stage in Portugal for a collaboration with the Mathematics Department of the University of Porto.