Introduction to optimal control theory

These are lecture notes of the introductory course in Optimal Control theory treated from the geometric point of view. Optimal Control Problem is reduced to the study of controls (and corresponding trajectories) leading to the boundary of attainable sets. We discuss Pontryagin Maximum Principle, basic existence results, and apply these tools to concrete simple optimal control problems. Special sections are devoted to the general theory of linear time-optimal problems and linear-quadratic problems