  The paper deals with the optimal control problem described by second order
evolution differential inclusions; to this end first we use an auxiliary
problem with second order discrete and discrete-approximate inclusions. Then
applying infimal convolution concept of convex functions, step by step we
construct the dual problems for discrete, discrete-approximate and differential
inclusions and prove duality results. It seems that the Euler-Lagrange type
inclusions are "duality relations" for both primary and dual problems and that
the dual problem for discrete-approximate problem make a bridge between them.
Finally, relying to the method described within the framework of the idea of
this paper a dual problem can be obtained for any higher order differential
inclusions. In this way relying to the described method for computation of the
conjugate and support functions of discrete-approximate problems a Pascal
triangle with binomial coefficients, can be successfully used for any "higher
order" calculations.
