Necessary optimality conditions for Lagrange problems involving ordinary control systems described by fractional Laplace operators

Abstract

In this paper, optimal control problems containing ordinary nonlinear control systems described by fractional Dirichlet and Dirichlet–Neumann Laplace operators and a nonlinear integral performance index are studied. Using smooth-convex maximum principle, the necessary optimality conditions for such problems are derived.

Optimal Control of a Nonlinear PDE Governed by Fractional Laplacian

“…2). The necessary optimality conditions for one-dimensional problem (1)-( 2) have been derived in [23] and [27] by using Dubovitskii-Milyutin approach [23] and a smooth-convex extremum principle [27]. In order to obtain results of such a type in the case of Ω ∈ R N more advanced investigations are required.…”