Variational Calculus and Optimal Control of Ordinary Differential Equations: Fall 2015

Course information

Please note

This course can be combined with the reading course on Convex Analysis to match a full 7.5 stp. course.


After modelling of processes by ordinary differential equations often the next step is to analyse the controllability or the optimal control of such a system. Typical examples might be vibration control in multi-body production machine models, the path-planning for industrial robots or autonomous vehicles, or medical applications like finding the optimal drug dosage. The mathematical theory behind these application problems is the main content of the lectures. In the first part we will study variational calculus, discussing topics like the Euler equation, first and second variations, and regularity of extremals. The second part is devoted to optimal control, here we will address topics like controllability, bang-bang controls, and Pontryagin’s maximum principle. The third part of the lectures covers numerical methods for optimal control problems.

Tentative lecture schedule

  • Mo. 24 to Fr. 28 and Mo. 31: 10.00-12.00
  • Tue. Sept. 1 : 12.00-14.00
  • Wed. Sep. 2 to Fri. Sep. 4: 10.00-12.00
  • Mo. Sep. 7: 14.00-16.00
  • Tue. Sep. 8: 10.00-12.00
  • Wed. Sep. 9: 12.00-14.00


2015-08-26, Dietmar Josef Hömberg