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

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, multi-controls, and the functional in suitable topologies.

This is a preprint of a paper whose final and definite form will be published in Journal of Optimization Theory and Applications, ISSN 0022-3239 (print), ISSN 1573-2878 (electronic). Submitted: 26-Dec-2014; Revised: 14-Apr-2015; Accepted: 19-Apr-2015

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• Fractional conservation laws in optimal control theory
• Approximate Controllability of Fractional Delay Dynamic Inclusions with Nonlocal Control Conditions
• Approximate Controllability of Fractional Nonlocal Delay Semilinear Systems in Hilbert Spaces

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