# TMA4505 Variational Calculus and Optimal Control of Ordinary Differential Equations: Fall 2014

## Course information

- Lectures: Dietmar Hoemberg
- Dates: 14.10–31.10
- Please contact anton.evgrafov@math.ntnu.no if you plan to participate

## Synopsis

After modelling of processes by ordinary differential equations often the next step is to analyse the controllability of the optimal control of such a system. Typical examples might be vibration control in multi-body production machine models, the path-planning for industrial robots or autonomous vehicles, or medical applications like finding the optimal drug dosage. The mathematical theory behind these application problems is the main content of the lectures. In the first part we will study variational calculus, discussing topics like the Euler equation, first and second variations, and regularity of extremals. The second part is devoted to optimal control, here we will address topics like controllability, bang-bang controls, and Pontryagin’s maximum principle. The third part of the lectures covers numerical methods for optimal control problems.

## Practicalities

- Time: 12.15 to 13.45, Oct 14-31
- Location: K24 in Chemistry building 3 (
*except for Thursday 23 and Monday 27 October*) - Location: 922 in math building (
*Thursday 23 and Monday 27 October*)