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

2020 Progress in Fractional Differentiation and Applications  
The present paper investigates 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 explored using two approaches: a reverse Hilbert uniqueness method, generalizing the approach introduced by Lions in 1988, and a penalization method, which allows us to characterize the minimum energy control. Keywords:
more » ... ractional calculus and diffusion, Caputo derivatives and enlarged controllability, RHUM approach and minimum energy, fractional optimal control, zone and pointwise actuators.
doi:10.18576/pfda/060201 fatcat:z6aoaexmg5aetkyz2zdq7fxtfu