Optimal Solutions to Relaxation in Multiple Control Problems of Sobolev Type with Nonlocal Nonlinear Fractional Differential Equations

Amar Debbouche (), Juan J. Nieto () and Delfim F. M. Torres ()
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Amar Debbouche: Guelma University
Juan J. Nieto: Universidad de Santiago de Compostela
Delfim F. M. Torres: University of Aveiro

Journal of Optimization Theory and Applications, 2017, vol. 174, issue 1, No 3, 7-31

Abstract: 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.

Keywords: Fractional optimal multiple control; Relaxation; Nonconvex constraints; Nonlocal control conditions; Sobolev-type equations; 26A33; 34B10; 49J15; 49J45 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10957-015-0743-7

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