Practical Course Optimal Control [MW2225]

Announcements
Key Facts
Contact Tuğba Akman, M.Sc.
Felix Schweighofer, M.Sc.
Language of Instructions English
Language of Materials English
Type / ECTS Lab Course / 4 (Elective Lab Module)
Semester Winter Semester
Time and Place Friday, 9.00-12.00, digital (TUM-Online)
Details
Prerequisites Required:

  • Basic experience with procedural programming in Matlab (functions, loops, matrix/vector operations, …)
  • Basic understanding of dynamic systems, preferably aircraft dynamics

Recommended:

Registration TUM-Online/PAS
Content / Educational Objectives The practical course on optimal control gives practical insight in the methods and implementation of optimal control problems for engineering applications. The optimal control problems are implemented and solved in the MATLAB development environment. The course is divided into the following lectures:

  • Introduction to MATLAB – on demand, prior experience recommended
  • Modeling of a dynamic system
    • basic flight dynamics modeling
    • implementation of the model dynamics
  • Simulation of a dynamic system
    • initial value problems
    • numerical integration using Runge-Kutta methods
    • implementation of integration methods
  • Unconstrained optimization
    • numerical methods for unconstrained parameter optimization problems
    • implementation of optimization algorithms
  • Constrained optimization
    • numerical methods for constrained parameter optimization problems
    • extension of the Matlab code w.r.t. equality and inequality constraints
  • Optimal control with multiple shooting and finite differences
    • direct transcription of optimal control problems
    • implementation of shooting methods for multi-phase constrained optimal control problems
  • Optimal control with multiple shooting and analytic derivatives (sensitivities)
    • efficient evaluation of derivatives in direct optimal control
    • implementation of sensitivity equations
  • Optimal control with local collocation
    • reduction of sensitivities by full discretization
    • impact on problem sparsity
    • efficient implementation of local collocation methods
  • Optimal control with pseudospectral methods (global collocation) – depending on timely progress
Teaching Methods / Materials
  • Theoretical background and methods:
    • independent preparation using lecture notes
    • presentation as an introduction to each chapter/assignment
  • Practical programming exercises:
    • to be solved individually or in groups during the weekly appointment
    • interactive video conference
    • supported by tutors
Exam The online course is concluded by a final written exam (60 min) covering all chapters. This exam will take place on campus.
Reference Literature