Regional boundary controllability of time fractional diffusion processes

TL;DR

This paper investigates how to control fractional diffusion systems within specific regions using boundary inputs, establishing conditions for controllability, optimal control strategies, and linking internal and boundary controllability.

Contribution

It introduces new characterizations of strategic actuators and optimal control methods for fractional diffusion systems with regional boundary controllability.

Findings

Characterization of strategic boundary actuators

Methods for minimum energy control

Connection between internal and boundary controllability

Abstract

In this paper, we are concerned with the regional boundary controllability of the Riemann-Liouville time fractional diffusion systems of order $\alpha\in (0,1]$. The characterizations of strategic actuators are established when the systems studied are regionally boundary controllable. The determination of control to achieve regional boundary controllability with minimum energy is explored. We also show a connection between the regional internal controllability and regional boundary controllability. Several useful results for the optimal control from an implementation point of view are presented in the end.