After successful completion of the course, students are able to...

After successful completion of the course, the students will be familiar with the Lagrangian and the Hamiltonian formalisms, typical Optimal Control problems, the principle of dynamical programming and the Hamilton-Jacobi-Bellman equations. They will be able to formulate and apply the Pontryagin maximum principle in order to solve classical problems in Control as well as in Calculus of Variations (after transforming them into Optimal Control problems). Finally, they get acquainted with the viscosity theory of PDE and the Eikonal equation. 

Topics:
1. Reminders from Calculus of Variations. Euler-Lagrange Equation
2. Hamiltonian formalism – Legendre transformation
3. Variational problems with constraints
4. Introduction to Optimal control. Lagrange, Mayer and Bolza formulations
5. Pontryagin Maximum Principle and applications
6. Principle of dynamical programming. Hamilton-Jacobi-Bellman equation
7. Introduction to viscosity solutions. Eikonal equation.

Lectures and exercises

This updated course is similar in content to WS2023 AKANA AKOR Calculus of Variation and Optimal Control.  It is not possible for both courses (WS2023 and WS2024) to be ackowledged for ECTS

Continuous evaluation and oral Exam

Students with a good background in Analysis/Optimization, motivated by modern trends in Mathematics, are encouraged to take this course.