Necessary optimality conditions for Lagrange problems involving ordinary control systems described by fractional Laplace operators - Kamocki, Rafał (Nonlinear Analysis: Modelling and Control, 2020)
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.
Keywords: smooth-convex extremum principle; spectral representation of a self-adjoint operator; fractional Laplace operator; Dirichlet and Dirichlet–Neumann boundary conditions