OPTIMIZATION OF THE NICOLETTI BOUNDARY VALUE PROBLEM FOR SECOND-ORDER DIFFERENTIAL INCLUSIONS

The paper is devoted to optimal control of the second-order Nicoletti boundary value problem (BVP) with differential inclusions (DFIs) and duality. First, we formulate the optimality conditions for the problem posed, and then, based on the concept of infimal convolution, the dual problems. It turns out that the Euler-Lagrange type inclusions are ”duality relations” for both primal and dual problems, which means that a pair consisting of solutions to the primal and dual problems sat-isfies this extremal relation, and vice versa. Finally, as an application of the results obtained, we consider the second-order Nicoletti BVP with polyhedral DFIs.