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On the existence of optimal solutions to the Lagrange problem governed by a nonlinear Goursat-Darboux problem of fractional order

Majewski Marek

Opuscula Mathematica

2023

Vol. 43, no. 4

547--558

In the paper, the Lagrange problem given by a fractional boundary problem with partial derivatives is considered. The main result is the existence of optimal solutions based on the convexity assumption of a certain set. The proof is based on the lower closure theorem and the appropriate implicit measurable function theorem.

Existence of optimal control for multi-order fractional optimal control problems

Kamocki Rafał

Archives of Control Sciences

2022

Vol. 32, No. 2

279--303

In this article we focus on optimal control problems involving a nonlinear fractional control system of different orders with Caputo derivatives, associated to a Lagrange cost functional. Based on a lower closure theorem for orientor fields combined with Filippov’s approach, we derive an existence result for at least one optimal solution for such a problem.