Sufficient Conditions of Optimality for Second Order Differential Inclusions

Abstract

In this paper we are concerned with the Bolza problem (PC) for second order differential inclusions (SODIs). The aim is to derive sufficient conditions of optimality for a problem (PC ). The basic concept of obtaining these conditions is the locally adjoint mappings (LAMs). Besides the transversality conditions, approaches to the general problem therefore involve distinctive Euler-Lagrange and Hamiltonian kind of adjoint inclusions. Furthermore, the aim of the considered “linear” problem with SODIs is to show the reader, by example, how the obtained results can be applied in practice.