Welcome to Optimal Control


Optimal control is the problem of finding control strategies for a dynamic system such that a certain performance function is minimized (or maximized). The subject stems from the calculus of variations and was developed into an independent discipline during the early 1950's mainly due to two discoveries: the maximum principle by L.S. Pontryagin and dynamic programming by R. Bellman. Optimal control finds its application in a variety of areas including engineering, economics, biology and logistics. 

The course has two main parts, which in headlines are: (1) Foundation of optimal control, and (2) Special topics. If time permits we will also discuss numerical implementation.

In the first part of 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 Hamilton-Jacobi-Bellman (HJB) equation and the (Pontryagin) maximum principle. We show how the dynamic programming principle works for an optimal control problem by using the HJB equation to solve linear quadratic control problems. Moreover, we apply the maximum principle to linear quadratic control problems. We end this part by introducing the notion of viscosity solution to the HJB equation.

In the second part of the course we will give an introduction to two areas of optimal control: singular optimal control where higher order conditions such as the generalized Legendre–Clebsch condition is used to obtain sufficient condition for local optimality, and optimal control of Markov processes where the state variables are not known with certainty (they are the outcome of stochastic differential equations). Finally, if time permits we will discuss software solutions for optimal control problems.  

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

Organizer: Associate Professor John Leth, jjl@es.aau.dk

Lecturers: Associate Professor John Leth


Time: 12 - 16 August, 2019

Place: TBA

Zip code: 9220

City: Aalborg Øst

Number of seats: 50

Deadline: 22 July, 2019  

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.