Optimal Control and Predictive Control


  • Current news are only available via the Moodle page of the lecture
  • Please register for the lecture via the TU Darmstadt TUCaN System. If you experience problems registering, contact Dr.-Ing. Eric Lenz

General Information about the Course

Lecturer Prof. Dr.-Ing Rolf Findeisen
Assistants Felix Häusser
Hoang Hai Nguyen
Dr.-Ing. Janine Matschek
Semester SoSe (2+1)
Teaching language English
Prerequisit Fundamental knowledge in control and systems theory, with a focus on state space formulations.
Form of examination written, oral
Depending on the number of participants the exam will be oral or written. The form of the exam will be announced shortly after the registration period.
Old exams Example exams will be provided via Moodle at the end of the lecture.
Subsequent lectures Starting in the winter term 2021 we will offer the lecture model predictive control.
Recommended literature Optimal Control
  • R. Bellman. Dynamic Programming. Princeton University Press, Princeton, New Jersey, 1957.
  • L.D. Berkovitz. Optimal Control Theory. Springer-Verlag, New York, 1974.
  • D.P. Bertsekas. Dynamic Programming and Optimal Control. Athena Scientific Press. 2nd edition, 2000.
  • L.M. Hocking. Optimal Control. An Introduction to the Theory with Applications. Oxford Applied Mathematics and Computing Science Series. Oxford University Press, Oxford, 1991.
  • J.L. Troutmann. Variational Calculus and Optimal Control. Undergraduate Texts in Mathematics. Springer, 1991.
  • S. Boyd, L. Vandenberghe. Convex Optimization. Cambridge University Press, 2004.
  • J. Nocedal, S. Wright. Numerical Optimization. Springer, 2006.
Model Predictive Control
  • J.B. Rawlings, D.Q. Mayne, M. Diehl. Model Predictive Control: Theory and Design, 2009.

Content of the Lecture

Goal and Content of the Lecture

Optimal control approaches, like model predictive control, are one of the most versatile, flexible and most often used modern control approaches by now. Fields of applications span from robotics, autonomous driving, aerospace systems, energy systems, chemical processes, biotechnology, up to biomedicine. The lecture provides an introduction to fundamentals of optimal control, focusing on the method and theoretical base. It furthermore provides an outreach towards efficient numerical solution strategies and model predictive control.


  • Application examples from various fields such mechatronics, robotics, electrical systems, chemical processes, economics, as well as aeronautics
  • Review of nonlinear programming
  • Dynamic programming, the principle of optimality, Hamilton-Jacobi-Bellman equation
  • Pontryagin maximum principle
  • Infinite and finite-horizon optimal control, LQ optimal control
  • Numerical solution approaches for optimal control problems
  • Introduction to model predictive control (MPC)


All materials of the lecture and exercises are provided via Moodle.
Exam Summerterm 2022
Form of exam written or oral
Date September
Time tba
Room tba
Permitted resources
  • pen
  • handwritten formula sheet, 4 pages/2 sheets both sided
Access to written exam tba