In this thesis, we explore the efficiency of different direct discretization strategies to find numerical solutions to re-entry optimal control problems with minimum heating. The first part of this thesis is dedicated to introducing the theoretical grounds of this work. We focus on SQP methods and the nonsmooth Newton method to solve nonlinear optimization problems numerically, and so-called first discretize, then optimize or direct discretization strategies for optimal control problems. The distinction between full and reduced discretization methods will be key to the development of different numerical strategies and the discussion on their efficiency in later chapters. The particularly sparse structure of the dynamics yielded by the application of the method of lines to PDE constrained optimal control problems is also illustrated here. The second part of the thesis is dedicated to the models, definitions and approximations needed to compose atmospheric re-entry trajectory problems with thermodynamic constraints, in order to explore the application of our methodologies to different problems that may arise in this context. In the third part of the thesis, the results of the application of a reduced discretization approach with the software OCPID-DAE1 to different re-entry optimal control problems are presented. The results show the robust applicability of this method to various problems featuring different scenarios, parameter optimization and coupled ODE-PDE problems. In the last part of the thesis, our newly implemented strategy for the exploitaiton of the structure yielded by a full discretization approach with a nonsmooth Newton method and PDE discretization through the method of lines is presented. The efficiency of this strategy is demonstrated through its application to quadratic and nonlinear heat equation control problems. We consider as well the application of this method to a re-entry temperature control problem with a controllable active cooling system. The computational results show that while reduced discretization is a viable and robust option for smaller trajectory problems, a structure-exploiting method is necessary in order to tackle large PDE constrained optimal control problems.    «

In this thesis, we explore the efficiency of different direct discretization strategies to find numerical solutions to re-entry optimal control problems with minimum heating. The first part of this thesis is dedicated to introducing the theoretical grounds of this work. We focus on SQP methods and the nonsmooth Newton method to solve nonlinear optimization problems numerically, and so-called first discretize, then optimize or direct discretization strategies for optimal control problems. The dis...    »