Numerical Optimal Control


Moritz Diehl (Lecture)
Robin Vujanic, Peter Hokayem (Exercise Supervision and Assistance)
ETH Zurich, Spring Semester 2011


Contents:   Objectives  -  Topics  -  Script  -  Schedule  -  Examination
+ Objectives

This lecture is aimed at all master or PhD students in the exact sciences, mathematics, and engineering that are interested in developing and using numerical methods for optimal control. It introduces the attendants into both, well-known classical ideas as well as recent algorithmic developments that are important for understanding and contributing to optimal control software. It will introduce into the technical vocabulary in the field, discuss the relevant mathematical concepts, and teach the participants in accompanying computer exercise sessions to implement and use the methods.
Poster Announcement
+ Topics

Topics to be covered in the course are:

- nonlinear optimal control problem formulations
- discrete time vs continuous time formulations
- dynamic programming
- The linear quadratic regulator (LQR)
- linear quadratic optimal control with constraints
- Pontryagin's maximum principle and calculus of variations
- direct methods, sequential and simultaneous
- collocation, direct single and multiple shooting
- sensitivities, forward and adjoint
- inexact SQP and SCP methods for optimal control
- QP linear algebra: condensing, sparse factorizations, LQR and Kalman recursions
- parametric optimization and real-time iterations
- existing optimal control software (e.g. ACADO Toolkit)
+ Script

In parallel with teaching the course, M. Diehl writes a Latex Script, a draft version of which is available here (and will be updated regularly):

DRAFT-PDF-SCRIPT (Status of May 9, basis for exam)

PDF-SLIDES for Embedded Optimization on May 5/6

PDF-SLIDES for the Lifted Newton Method on April 8

PDF-SLIDES for ACADO Introduction on April 8

+ Schedule

The course takes place on Thursday and Friday from 13:15-15:00, in selected weeks. Each Friday, it is followed by a computer exercise, from 15:15-17:00. There are no "Testate" and it is not required that the students appear in every lecture or computer exercise. Self study of the script or other books and solving the computer exercises at home is possible. However, it is strongly recommended to do the computer exercises which constitute an important part of the course. The exercise sessions are designed for independent work on the exercise sheets with the possibility to ask questions. They will be supervised by Robin Vujanic and Moritz Diehl.
The lecture and exercise dates are:
  • Feb 24: Background in Simulation (Chapter 1)
  • Feb 25: Background in Optimization (Chapter 2)
  • Feb 25 (exercise): Nonlinear Programming and Single Shooting. Exercise Sheet 1
  • March 10: Background in Optimization (Chapter 2/3)
  • March 11: Newton-Type Optimization (Chapter 3) and Optimal Control (Chapter 5)
  • March 11 (exercise): Runge-Kutta Integrator and Gauss-Newton Algorithm. Exercise Sheet 2
  • March 17: Algorithmic Differentiation (Chapter 4)
  • March 18: Structure of the Optimal Control Problem (Chapter 5 and 6)
  • March 18 (exercise): Gauss-Newton vs. BFGS, and Reverse Differentiation. Exercise Sheet 3
  • March 31: Sparsity Exploitation
  • April 1: Overview and Dynamic Programming
  • April 1: (exercise): Simultaneous Optimal Control with Gauss-Newton. Exercise Sheet 4
  • April 7: Continuous Time Optimal Control: HJB and Pontryagin
  • April 8: The Lifted Newton Method / Numerics within ACADO
  • April 8: (exercise): Installing and Using ACADO Toolkit. Exercise Sheet 5.
    Optional extra exercise: Dynamic Programming - Exercise Sheet 5a.
  • May 5: Real-Time Optimization
  • May 6: Real-Time Optimization
  • May 6: (exercise): Pontryagin and the Indirect Approach. Exercise Sheet 6.
  • May 12: Estimation Problems / Lecture Summary
  • May 13: Exam Preparation and Presentation of Projects
  • May 13: (exercise): Real-Time Iterations and Model Predictive Control. Exercise Sheet 7.
  • May 20
    • WRITTEN EXAM
+ Examination

On May 20, 2011, at 13-15, in room ETZ E 6, a written closed book examination of two hours takes place. In addition to the exam, as a second condition to obtain the credit points, a short project report of 2-3 pages shall be handed in beforehand that contains the description of a self-chosen optimal control problem and a self-written computer code for its numerical solution (using the software used and developed in the computer exercises. The final mark of the course is a weighted average of the written exam (75%) and the project report (25%).
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Last updated and validated January 20, 2011