Convex optimization of second order discrete and differential inclusions with inequality constraints

The paper deals with a Bolza problem of optimal control theory given by second order convex differential inclusions (DFIs) with second order state variable inequality constraints (SVICs). The main problem is to derive sufficient conditions of optimality for second order DFIs with SVICs. According to the proposed discretization method, problems with discrete-approximation inclusions and inequalities are investigated. Necessary and sufficient conditions of optimality including distinctive "transversality" condition are proved in the form of Euler-Lagrange inclusions. Construction of Euler-Lagrange type adjoint inclusions is based on the presence of equivalence relations of locally adjoint mappings (LAMs). Moreover, in the application of these results, we consider the second order "linear" differential inclusions.