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Optimization of higher-order differential inclusions with special boundary value conditions. (English) Zbl 1481.49022

Summary: The paper is devoted to Lagrange problem of optimal control theory with higher-order differential inclusions (HODI) and special boundary conditions. Optimality conditions are derived for HODIs, as well as for their discrete analogy. In this case, discretization method of the second-order differential inclusion is used to form sufficient optimality conditions for HODIs and periodic boundary conditions, the so-called transversality conditions. And to construct an Euler-Lagrange-type inclusion, a locally adjoint mapping is used, which is closely related to the coderivative concept of Mordukhovich. In turn, this approach requires several important equivalence results concerning LAMs to the discrete and discrete-approximate problems. The results obtained are demonstrated by the optimization of some “linear” optimal control problems, for which the Weierstrass-Pontryagin maximum principle and transversality conditions are formulated.

MSC:

49K15 Optimality conditions for problems involving ordinary differential equations
90C26 Nonconvex programming, global optimization
93C15 Control/observation systems governed by ordinary differential equations
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