Enlarged Controllability and Optimal Control of Sub-Diffusion Processes with Caputo Fractional Derivatives

TL;DR

This paper explores advanced control strategies for fractional diffusion processes using Caputo derivatives, introducing new definitions and methods to extend controllability and optimize control energy.

Contribution

It introduces a novel definition of enlarged controllability for fractional diffusion equations and applies two approaches to characterize minimum energy controls.

Findings

Extended controllability concepts for fractional diffusion

Characterized minimum energy controls via two methods

Generalized Lions' approach for fractional systems

Abstract

We investigate the exact enlarged controllability and optimal control of a fractional diffusion equation in Caputo sense. This is done through a new definition of enlarged controllability that allows us to extend available contributions. Moreover, the problem is studied using two approaches: a reverse Hilbert uniqueness method, generalizing the approach introduced by Lions in 1988, and a penalization method, which allow us to characterize the minimum energy control.