OPTIMAL CONTROL OF SEMILINEAR HIGHER-ORDER DIFFERENTIAL INCLUSIONS

The paper investigates an optimal control problem described by higher-order differential inclusions (DFIs). In terms of the Euler-Lagrange type adjoint DFIs and Hamiltonian, a sufficient optimality condition for higher-order DFIs is derived. At the same time, when constructing the Euler-Lagrange type adjoint DFI, without using tra-ditional approaches to constructing an adjoint operator and a discrete -approximate method, the new method of adjoint DFI of Mahmudov for "higher-order problems " is used. It is shown also that the adjoint DFI for the first order DFI coincides with the classical Euler-Lagrange inclusion, and the optimality conditions coincide with the results of Rockafellar on the Mayer problem with first order DFIs. Thus, the obtained results are universal in the sense that sufficient optimality conditions can be formu-lated for a DFI of any order. At the end of the paper, problems with a high-order polyhedral DFIs and higher-order linear optimal control prob-lems are considered, the optimality conditions of which are transformed into the Pontryagin maximum principle. Also, for high-order polyhedral optimization, from the point of view of abstract economics, non-negative adjoint variables can be interpreted as the price of a resource.