Summer School on Direct Methods for Optimal Control of Nonsmooth Systems

Tuesday, September 12, 2023, 9:00 - Friday, September 15, 2023, 16:00

Kollegiengebäude I, HS 1015, Platz der Universität 3, D-79098 Freiburg

Lectures: Moritz Diehl and Armin Nurkanović

Guest Lectures: Christian Kirches (TU Braunschweig)

Exercises: Jonathan Frey, Florian Messerer, and Anton Pozharskiy


We are happy to announce our four-day summer school on Direct Methods for Optimal Control of Nonsmooth Systems for industrial and academic researchers, in particular PhD and master students in mathematics, engineering, physics, and computer science.


Participation fee: 200 EUR (free of charge for master’s students from the University of Freiburg).

Registration link 

Registration link for students from the University of Freiburg

Registration Deadline12.08.2023
The registration is closed. However, we have created a waiting list and you are still encouraged to register. If free places become available, we will notify you via e-mail.

Apply for a scholarship: We offer five “free-tuition” scholarships that cover the registration fee for PhD and master's students who are not affiliated with the University of Freiburg.
To apply for the scholarship, fill out the form and send one or two recommendation letters (e.g. from your supervisor) recommending you and your talents and supporting your attendance at the summer school to The application deadline for the scholarship is July 15, 2023. We will notify you about the result of the application before July 25, 2023.


This four-day intensive course aims to provide both theoretical background and hands-on practical knowledge in formulating and numerical methods to solve optimal control problems with nonsmooth differential equation models with switches and state jumps. Nonsmooth dynamical systems arise in robotics, contact-implicit optimization, chemical engineering, biology, mechatronics, aerospace, or as soon as some if-else statements, switches, and state jump are encoded in the systems’ dynamics.


Check out our flyer!


Course Topics 

  • Recap on theory and algorithms for nonlinear programming
  • Modelling with differential-algebraic equations 
  • Numerical simulation and direct collocation
  • Introduction to nonsmooth differential equations and hybrid systems
  • Modelling with Filippov systems – Stewart’s and step formulation
  • Finite Elements with Switch Detection (FESD) for Filippov systems
  • Time-freezing 1: Elastic impacts and hybrid automatons with hysteresis​​​​​
  • Approximate propagation of normal distributions for stochastic optimal control of nonsmooth systems
  • Time-freezing 2: Rigid bodies with friction and inelastic impacts
  • Theory of Mathematical Programs with Complementarity Constraints (MPCCs)
  • Relaxation and smoothing-based algorithms for MPCCs
  • Pivoting-based algorithms for MPCCs
  • Formulating nonsmooth optimal control problems and summary



For more details please visit the course page.


You will receive the payment details for your registration via Email.  The fee will cover, among others, the expenses for the catering, the welcome reception, and the dinner. 
Please notice that the participation will be limited to approximately 50 people (first come first serve).

A confirmation email will be sent out approximately on a daily base. 

In case you have any questions feel free to contact:




This course has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 953348 and from the Bundesministerium für Wirtschaft und Klimaschutz (BMWK.IIC6) via the project "EnEff:Wärme: WOpS - Wärmefluss-Optimierung zur Sektorenkopplung in Fernwärmenetzen mitttels MPC unter Berücksichtigung eines strommarktorientierten Betriebes, Teilvorhaben: Modellierung, Simulation und Betriebsführung", with the project number 03EN3054A.