Yuri Sachkov is the Chief of Control Processes Research Center at Program Systems Institute, Russian Academy of Sciences, in Pereslavl-Zalessky, Russia. His research interests include optimal control theory, sub-Riemannian, sub-Finsler and sub-Lorentzian geometry, and their applications to mechanics, robotics, and vision. Prof. Sachkov is a world renown expert in geometric control theory and has authored more than 80 research papers in leading international and Russian journals. Sachkov has also authored two well-known books: (with A.A. Agrachev) Control Theory from the Geometric Viewpoint, Springer (c) 2004, and Controllability and symmetries of invariant systems on Lie groups and homogeneous spaces (in Russian), Moscow, Fizmatlit, 2007. He is a managing editor of Journal of Dynamical and Control Systems, Springer.

List of figures.- 1. Introduction.- 2. Controllability problem.- 3. Optimal control problem.- 4. Solution to optimal control problems.- 5. Conclusion.- A. Elliptic integrals, functions and equation of pendulum.- Bibliography and further reading.- Index.