Moritz Diehl

University of Freiburg

Monday, February 16, 2026, 9:00 - Friday, February 20, 2026, 12:00

Room: K4.438, Sem Sælands vei 6, 7034 Trondheim, Norway

This course is intended for PhD students with interest in numerical methods for optimal control. We will briefly cover the basics and and then focus on some recently developed methods for non-standard optimal control problems.

Topics:

• Numerics for non-linear optimal control
• Real-time non-linear optimal control
• Robust non-linear optimal control
• Non-smooth optimal control

Lectures take place in morning sessions from 9:00-12:00 on 16, 17, 19 & 20 Feb 2026. Exercises will take place in afternoon sessions from 13:00-15:00 on 16, 17 and 19 Feb 2026 and are supervised by Archana Kumaraswamy. Note: course break on Wednesday, Feb 18 (no lectures, no exercises, but insteady PhD defense of Simen Bjorvand)

Schedule with Lecture Slides and Exercises

• Monday 9:00 - Introduction / Numerical Optimization (PDF)  
• Monday 11:00 - Numerical Optimal Control: Smooth, Nonsmooth, and Robust (PDF)
• Monday 13:00 - Exercise 1 - Nonlinear Optimization with CasADi and IPOPT. Code Ex 1. Solution Ex 1.
• Tuesday 9:00 - Numerical Optimal Control (PDF) , lifted-newton
• Tuesday 11:00 - Nonlinear Model Predictive Control and Real-Time Optimization (PDF), acados-pitch
• ,Tuesday 13:00 - Exercise 2 - Nonlinear Model Predictive Control with IPOPT and acados. Code Ex 2. Solution Ex 2. 
• Thursday 9:00 - Robust Optimization (PDF) 
• Thursday 11:00 -  Robust Dynamic Optimization (PDF)
• Thursday 13:00 - Exercise 3 - OCP Playground. Code Ex3.
• Friday - 9:00 - OCP Project Presentations. 9:30 Mixed Integer Nonlinear Optimal Control (PDF), 10:00 Nonsmooth Optimal Control via Finite Elements with Switch Detection (FESD) (PDF), 11:00 Time-Freezing for Systems with Jumps and Hysteresis (PDF)
• Bonus - Exercise 4 - Robust MPC with ZORO in acados. Code Ex 4. Solution Ex 4.

Software

For the exercises, we will use Python with CasADi and acados.

To set-up your Python environment, you can run:

pip install numpy scipy matplotlib casadi 

To install acados, follow the instructions at: https://docs.acados.org/installation/index.html.

For the acados Python interface, see: https://docs.acados.org/python_interface/index.html.

To Windows users, we recommend to install acados via WSL (Windows Subsystem for Linux).