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. 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 optimization algorithms and the application of optimal control. Here, we will concentrate on convex optimization techniques (dual decomposition, admm) 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.

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

Organizer: Professor Rafael Wisniewski

Lecturers: Associate Professor Jan Østergaard, Department of Electronic Systems, Assistant Professor John Leth, Department of Electronic Systems, Assistant Professor Christoffer Sloth, Department of Electronic Systems and Professor Rafael Wisniewski, Department of Electronic Systems


Time: 24-28 August, 2015

Place: Aalborg University

Zip code:


Number of seats: 50

Deadline: 3 August, 2015