Welcome to Control and Optimization

Description: Optimal control is the problem of finding control for a dynamic system such that a certain performance function is minimized. The subject stems from the calculus of variations. The prompt development of optimal control in 1950s owns two inventions: the maximum principle by L.S. Pontryagin and dynamic programming by R. Bellman. Today, the stress is on developing efficient numerical methods for solving a class of optimal control problems (herein convex optimization). Optimal control finds its application not only in engineering, but also in economics, biology and logistics.

The course has two main parts, which in headlines are: Optimal Control, Optimization and Applications.

In the course, we will concentrate on the foundation of optimal control. We will discuss necessary and sufficient condition for optimality, and various types of constraints. We will address the question of existence of optimal strategies.

We cover two main results in optimal control theory, the Bellman (or Hamilton-Jacobi-Bellman) equation and the (Pontryagin) maximum principle. We show how the dynamic programming principle works for an optimal control problem by using the Bellman equation to solve linear quadratic control problems. Moreover, we apply the maximum principle to linear quadratic control problems. The second part of the course will be devoted to the optimization algorithms and the application of optimal control. Here, we will concentrate on convex optimization techniques: conic optimization, dual decomposition, admm, as they provide tangible methods for solving (convex) optimization problems. We will discuss software for optimization of dynamical systems.

Prerequisites: A basic knowledge of mathematics as obtained through undergraduate engineering studies.

Organizer: Associate Professor John Leth.

Lecturers: Dr. Joachim Dahl, MOSEK ApS, Associate Professor Jan Østergaard, Department of Electronic Systems, Associate Professor John Leth, Department of Electronic Systems, Associate Professor Christoffer Sloth, Department of Electronic Systems, and Professor Rafael Wisniewski, Department of Electronic Systems


Time: 26. - 30. June 2017


Zip code:


Number of seats: 50

Deadline: 1. June 2017

Important information concerning PhD courses We have over some time experienced problems with no-show for both project and general courses. It has now reached a point where we are forced to take action. Therefore, the Doctoral School has decided to introduce a no-show fee of DKK 5,000 for each course where the student does not show up. Cancellations are accepted no later than 2 weeks before start of the course. Registered illness is of course an acceptable reason for not showing up on those days. Furthermore, all courses open for registration approximately three months before start. This can hopefully also provide new students a chance to register for courses during the year. We look forward to your registrations.