Mathematical Methods of Optimal Control Theory and Their Applications: The time and energy efficient train control problem

This master's thesis deals with the continuous optimal control problem, which is one of the most important applications of the differential equations theory. The aim of this work was to study the mathematical theory of the optimal control and the significant part was to show how Pontryagin's maximum principle and Bellman's principle of optimality can be used in the particular optimal control problems. The emphasis was mainly put on the time and energy efficient electrically powered train control problem, where the quadratic resistant function has been involved.