Free time optimization of higher order differential inclusions with endpoint constraints

The paper is devoted to the study of optimal control theory with higher order differential inclusions (HODIs) and a varying time interval. Essentially, under a more general setting of problems and endpoint constraints the main goal is to establish sufficient conditions of optimality for HODIs. Thus with the use of Euler–Lagrange and Hamiltonian type of inclusions and transversal conditions on the ‘initial’ sets, the sufficient conditions are formulated. Derivation of Euler–Lagrange inclusions and t₁-attainability conditions are real difficulties. Application of these results by solving some linear control problem (P_L) with third-order differential inclusions is illustrated. The Pontryagin maximum principle in problem (P_L) together with t₁-attainability condition holds.