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

Abstract

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.

Keywords

• existence of optimal control
• multi-order fractional control system
• lower closure theorem