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:
Part 1: Foundation (20%), Optimal Control (30%)
Part 2: Numerical Methods (30%) and Application (20%)
In the foundation part we will first concentrate on the calculus of variation, which is at 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. We will end this part with a discussion of one or more of the following subjects: discrete time version of the maximum principle, stochastic optimal control, and viscosity solutions.
The second part of the course will be devoted to the numerical methods and the application of optimal control. Here, we will concentrate on convex optimization techniques as they provide tangible methods for solving (convex) optimization problems. We will introduce to the subject of Model Predictive Control and its industrial applications. We will discuss software for optimization of dynamical systems.

Professor Rafael Wisniewski

Associate Professor John Bagterp Jørgensen, DTU Informatics
Jørgen Knudsen, 2-control
Associate Professor Cornean, Department of Mathematical Sciences, Aalborg University
Assistant Professor John Leth, Automation & Control, Aalborg University
Professor Rafael Wisniewski, Automation & Control, Aalborg University


September 23rd, September 24th, September 25th, September 30th, October 1st, and October 2nd, 2013.

Aalborg University
September 25: Fredrik Bajers Vej 7E/3-109

September 26: Fredrik Bajers Vej 7A/4-108
September 27: Fredrik Bajers Vej 7E/3-109
September 30: Niels Jernes Vej 12A/6-104
October 1: Niels Jernes Vej 12A/6-104
October 2: Niels Jernes Vej 12A/6-104

Zip code:


Number of seats:

September 2, 2013

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.