Sufficient Conditions of Optimality for Free Time Optimization of Third Order Differential Inclusions

Abstract

The present paper deals with the free time optimization problem described by third order differential inclusions (P-C) with endpoint constraints. In order to construct the optimality conditions for our problem (P-C), we obtain the optimality conditions for the discrete-approximation problem associated with the auxiliary differential problem (P-A) given by third order convex differential inclusions. Formulation of optimality conditions for problem (P-A) plays a substantial role in incorporating the Euler-Lagrange and Hamiltonian type inclusions and moreover by using distinctive t(1)-attainability conditions on the initial sets, the sufficient conditions for our main problem (P-C) are established.