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Title: Optimal Solutions to Relaxation in Multiple Control Problems of Sobolev Type with Nonlocal Nonlinear Fractional Differential Equations
Author: Debbouche, A.
Nieto, J. J.
Torres, D. F. M.
Keywords: Fractional optimal multiple control
Nonconvex constraints
Nonlocal control conditions
Sobolev-type equations
Issue Date: 2017
Publisher: Springer
Abstract: We introduce the optimality question to the relaxation in multiple control problems described by Sobolev-type nonlinear fractional differential equations with nonlocal control conditions in Banach spaces. Moreover, we consider the minimization problem of multi-integral functionals, with integrands that are not convex in the controls, of control systems with mixed nonconvex constraints on the controls. We prove, under appropriate conditions, that the relaxation problem admits optimal solutions. Furthermore, we show that those optimal solutions are in fact limits of minimizing sequences of systems with respect to the trajectory, multicontrols, and the functional in suitable topologies. © 2015, Springer Science+Business Media New York.
Peer review: yes
DOI: 10.1007/s10957-015-0743-7
ISSN: 0022-3239
Appears in Collections:CIDMA - Artigos
SCG - Artigos

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