Prof. Dr. Moritz Diehl  moritz.diehl (at) imtek.unifreiburg.de
The aim of this intensive twoweek intensive course is to give both theoretical background and handson practical knowledge with computational tools for optimal control with differential algebraic equation models.
Content
The course covers all topics relevant for the formulation and practical solution of optimal control problems (OCP) with differential algebraic equation models. It builds on concepts from both, numerical simulation of differential algebraic equations and nonlinear optimization. All lecture topics are accompanied by intensive computer exercises, for which we use the optimization modelling environment CasADi from MATLAB or Python. The first week, whose contents are optional for experienced participants, contains an introduction into using CasADi, into convex optimization and nonlinear programming and into algorithms for general nonlinear optimal control problems such as direct single and multiple shooting and direct collocation. The second week focuses on optimal control with differential algebraic equation (DAE) models. Topics comprise implicit integration methods, highindex DAE, invariants, Baumgarte stabilization, periodic problems and optimal control under uncertainty.
Towards the end of the course, each participant will start to work on a selfchosen application problem and the results will be presented in a short public presentation on the last day of the course.
The detailed schedule for the course can be found here.
Prerequisites, Workload and Evaluation
The course is self contained and can be followed by all quantitative scientists with solid mathematical background (calculus and linear algebra) and knowledge of dynamic systems. It is recommended for both industrial and academic practitioners of control and optimization as well as for master and PhD students of engineering, computer science, mathematics, and physics. The total workload is 90 hours including lectures, project work and selfstudy, and the course gives 3 ECTS credits. The final course evaluation is based 50% on the written exam and 50% on the project. A certificate of attendance can be given to participants not wishing to participate in the exam and/or project.
Time and place
The course takes place from Monday, February 15, 2016 to Friday, February 26, 2016, from 9:0018:00, in the main historical university building in the city center of Freiburg (Kollegiengebäude I, HS 1098, Platz der Universität 3, D79098 Freiburg). In the weekend, an optional excursion into the black forest is foreseen. The written exam takes place on Thursday, February 25, 9:0010:30. The final project presentations take place on Friday, February 26, 2016.
Registration
Participation in the course is limited to 60 places. A cost contribution of 300 Euro to cover coffee breaks and social events will be required by external participants. To apply for participation please fill in the following form before January 17, 2016:
People
This workshop is organized by Moritz Diehl, Andrea Zanelli, Dimitris Kouzoupis, Rien Quirynen, Robin Verschueren, Christine Paasch and with external teachers:
 Sebastian Gros (Chalmers)
 Joel Andersson (UW Madison)
 Joris Gillis (KU Leuven)
Video Lectures
Videos of the lectures given during the course are available upon request. If you are interested, please contact Andrea Zanelli (andrea.zanelli(at)imtek.unifreiburg.de).
Detailed Program and Material

week 1:
Monday  Tuesday  Wednesday  Thursday  Friday  
09:00 
Introduction into Optimization and CasADi 
Numerical Simulation and Derivatives 
Newton Type Optimization (part 1) 
Direct Single and Multiple Shooting (part 1) 
The Indirect Approach (part 1) 
10:30  Coffee Break  Coffee Break  Coffee Break  Coffee Break  Coffe Break 
11:00  
12:30  Lunch Break  Lunch Break  Lunch Break  Lunch Break  Lunch Break 
14:00 
Nonlinear Programming & 
Optimal Control Overview (part 1) 
Interior Point Methods (part 1) 
Direct Collocation (part 1 ) 
Optimal Control with TOMLAB 
15:30  Coffee Break  Coffee Break  Coffee Break  Coffee Break  Coffee Break 
16:00  Embedded Optimal Control with ACADO  
17:30  Extra Time  Extra Time  Extra Time  Extra Time  Extra Time 
18:00  End  End  End  End  End 

week 2:
Monday  Tuesday  Wednesday  Thurday  Friday  
09:00 
Differential Algebraic Equation (DAEs) Models (part 1 ) 
Optimal Control with DAEs (part 1) 
Optimal Control of Airborne Wind Energy Systems (part 1 ) 
Exam  
10:30  Coffee break  Coffee break  Coffee break  Coffee break  Coffee break 
11:00 
(solution ) 
Stability and Robustness Optimization for Periodic Systems (part 1 ) 
Projects 
Projects Presentation 

12:30  Lunch break  Lunch break  Lunch break 
Lunch break 
Lunch break 
14:00 
High Index DAEs and Index reduction (part 1) 
Periodic Optimal Control with DAEs (part 1) 
Projects  Projects 

15:30  Coffee break  Coffee break  Coffee break  Coffee break  
16:00  Projects  Projects  
17:30  Extra time  Extra time  Extra time  Extra time  
18:00  Project Commitments  End  End  End 
Social event Sunday, 21th of February
On the Sunday between the first and second week of the course, there will be a oneday hike in Waldkirch. To register, please fill out this form: https://goo.gl/EwpraD
Extra Material
Optistack demo files and install instructions
References
Numerical Optimization of Dynamic Systems  Moritz Diehl, Sebastien Gros.
Pictures from the Event