Home » Teaching » Aircraft Trajectory Optimization

Announcements

Key Facts

This lecture is part of the Munich Aerospace Teaching Collaboration between TUM and UniBw M.

Contact

Language, Format, and Materials

The class is given in English, on-site. We present the topics based on the lecture notes and encourage active participation. Lecture and exercise elements are interspersed during each course session.

Lecture and exercise materials, including slides, worksheets, and code examples, are distributed via the Moodle platform.

Course Type, Registration, and Exam

For aerospace students, the course is an Elective Lecture Module (3 ECTS). Please register via TUMonline (Lecture, Exercise). Note that only the lecture registration is linked to the Moodle course, and that we use the timeslots of both lecture and exercise interchangeably.

There will be an oral exam (30 min) at the end of the semester. Appointments will be announced or arranged in class. Usually there are two or three exam appointments ranging from early July to September.

Time and Place

The course takes place on Mondays, from 13:15 to 15:45, in room MW3618. We do not distinguish between the lecture and exercise timeslots.

The individual course sessions are relatively long. However, due to the collaboration with UniBw M, the last regular course appointment is scheduled for 2025-06-23.

Details

Prerequisites

Generally, we expect an interest in mathematics and optimization theory. For the aerospace aspects, the Introduction to Flight Mechanics and Control course or an equivalent level of aerospace knowledge is strongly recommended. However, experience shows that motivated students can participate without any specific aerospace background.

Content and Learning Goals

Aircraft trajectory optimization belongs to the mathematical field of optimal control. This means that the optimal control history and the optimal state history (and maybe other additional parameters) that minimize a given cost function for a given dynamic system need to be calculated. Thereby, all given initial and final boundary conditions as well as path equality and inequality constraints need to be fulfilled. This enables e.g. the calculation of noise minimal approach and departure trajectories for a given aircraft at a given airport considering the population distribution as well as any procedural requirements. In this lecture the students should learn how to solve such optimal control problems beginning with the modeling of the required dynamic system as well as the cost and constraint functions. In the next steps on the one side theoretical optimality conditions are derived for simple examples and on the other side discretization techniques for the solution of realistic problems are introduced. Afterwards, methods for the solution of the resulting sparse parameter optimization problem are presented. Finally, other aspects related to the implementation are introduced.

Topics:

  • Modeling of dynamic systems
  • Simulation methods
  • Optimal control theory
  • Numerical optimization
  • Direct discretization techniques
  • Generation of initial guesses
  • Aircraft related constraints and cost functions
  • Sensitivity analysis
  • Implementation aspects

Reference Literature