Weak Pontryagin's Maximum Principle for Optimal Control Problems Involving a General Analytic Kernel

Abstract

We prove a duality relation and an integration by parts formula for fractional operators with a general analytical kernel. Based on these basic results, we are able to prove a new Gronwall's inequality and continuity and differentiability of solutions of control differential equations. This allow us to obtain a weak version of Pontryagin's maximum principle. Moreover, our approach also allow us to consider mixed problems with both integer and fractional order operators and derive necessary optimality conditions for isoperimetric variational problems and other problems of the calculus of variations.

arXiv commentThis is a preprint whose final form is published by Elsevier in the book 'Fractional Order Systems and Applications in Engineering'. Submitted 10/Sept/2020; Revised 22/Nov/2020 and 18/May/2021; Accepted 05/Sept/2021

References in corpus (7)

• The Variable-Order Fractional Calculus of Variations
• On fractional calculus with general analytic kernels
• On some analytic properties of tempered fractional calculus
• General fractional calculus and Prabhakar's theory
• Integration-by-parts reductions of Feynman integrals using Singular and GPI-Space
• Distributed-Order Non-Local Optimal Control
• Surface measures and integration by parts formula on levels sets induced by functionals of the Brownian motion in ${\mathbb{R}}^n$

Cited by in corpus (1)

• A Necessary Optimality Condition for Extended Weighted Generalized Fractional Optimal Control Problems