THE LAGRANGE PROBLEM FOR DIFFERENTIAL INCLUSIONS WITH BOUNDARY VALUE CONDITIONS AND DUALITY

Abstract

The present article studies the duality of the Lagrange problem of optimal control theory with the boundary value constraints given by second-order polyhedral differential inclusions. Our primary aim is to establish results of duality for a boundary value problem with second-order differential inclusions. As a supplementary problem, we consider differential problems and formulate sufficient conditions of optimality, including particular transversality conditions incorporating the Euler-Lagrange type inclusions. After constructing the dual problem for second-order polyhedral differential inclusions, we prove that the adjoint Euler-Lagrange inclusion is simultaneously a dual relationship, which is satisfied by the pair of solutions of the primal and dual problems. Furthermore, solving numerical examples illustrates the application of these results.