Trajectory Optimization Problem: Parallel Aglorithm Developement and Its Application in Space Mission(1/2)

The objectives of this project are to develop and study the full-space quasi Lagrange-Newton-Krylov(FQLNK) algorithm for solving trajectory optimization problems arising from aerospace industrialapplications. Trajectory optimization problem can be mathematically described as an optimizationproblem constrained by a system of ordinary differential equations. As its name suggests, we firstconvert the constrained optimization problem into an unconstrained one by introducing the augmentedLagrangian parameters. The next step is to find the optimal candidate solution by solving theKarush-Kuhn-Tucker (KKT) condition with the Newton-Krylov method. To make our FQLNKalgorithm more efficient and robust, we will address some computational issues, including the efficientconstruction of KKT system, the robustness improvement of inexact Newton algorithm via nonlinearpreconditioning. We also will consider more general cases to meet the real launch vehicle mission need.These cases include the optimization with inequality, multi-objective optimization problems, anextension of 3D dynamic constraint case, and parallel implementation of the proposed aglorithm.