This project is a group award to the PIs and Professors V. Barbu and S. Stojanovic to study a wide range of topics in Optimal Control Theory. Hamiltonian inclusions with applications to antiperiodic functions and control of free boundary value problems are the main topics to be developed. These studies have applications to the design of control systems. A particular example arising in electro-photography will be studied at length due to its immediate technological applicability.