Aircraft Trajectory Optimization

Key Facts
Contact Prof. Dr. rer. nat. Matthias Gerdts
Tuğba Akman, M.Sc.
Felix Schweighofer, M.Sc.
Language of Instructions English or German, depending on students
Language of Materials English
Type / ECTS Lecture, Exercise / 3 (Elective Lecture Module)
Semester Summer Semester
Time and Place Note: The course starts on 2021-04-19.
Lecture: Mondays, 14.30-16.00, online (TUM-Online)
Exercise: Mondays, 16.00-17.00, online (TUM-Online)
Lab: Mondays, 17.00-18.30, online (TUM-Online)
Related Links TUM-Online: Lecture, Exercise, Lab
Content / Educational Objectives 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.

Table of Contents:

  • 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 in MATLAB
Teaching Methods / Materials For the lecture and the guided tutorial lecture notes are available. The theory can be deepened in a MATLAB computer tutorial, guided by FSD.
Exam Oral exam, 30 Minutes.
Reference Literature
  • John T. Betts, Practical Methods for Optimal Control and Estimation Using Nonlinear Programming, Advances in Design and Control, SIAM, 2009
  • Donald E. Kirk, Optimal Control Theory: An Introduction, Dover Pubn Inc, 2004
  • Matthias Gerdts, Optimal Control of ODEs and DAEs, De Gruyter, 2012

This lecture is part of the Munich Aerospace Teaching Collaboration.

ATO Lecture Image