Optimization of second order differential inclusions with boundary value conditions

The present paper studies the Lagrange (PL) and Bolza (PB) types problems of optimal control theory with a fixed time interval given by second order differential inclusions. Mainly our purpose is to derive sufficient optimality conditions for mentioned problems with second order differential inclusions. Sufficient conditions of optimality, including distinctive transversality ones, are proved by incorporating the Euler-Lagrange and Hamiltonian type of inclusions. The basic idea of obtaining optimal conditions is the use of locally adjoint mappings (LAM). Furthermore, application of these results are demonstrated in the second order "linear" optimal control problem.