6 research outputs found
Enlarged Controllability of Riemann-Liouville Fractional Differential Equations
We investigate exact enlarged controllability for time fractional diffusion
systems of Riemann-Liouville type. The Hilbert uniqueness method is used to
prove exact enlarged controllability for both cases of zone and pointwise
actuators. A penalization method is given and the minimum energy control is
characterized.Comment: This is a preprint of a paper whose final and definite form is with
'Journal of Computational and Nonlinear Dynamics', ISSN 1555-1415, eISSN
1555-1423, CODEN JCNDDM, available at
[http://computationalnonlinear.asmedigitalcollection.asme.org]. Submitted
10-Aug-2017; Revised 28-Sept-2017 and 24-Oct-2017; Accepted 05-Nov-201
Enlarged controllability and optimal control of sub-diffusion processes with Caputo fractional derivatives
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.publishe
Regional controllability and minimum energy control of delayed caputo fractional-order linear systems
We study the regional controllability problem for delayed fractional control systems through the use of the standard Caputo derivative. First, we recall several fundamental results and introduce the family of fractional-order systems under consideration. Afterward, we formulate the notion of regional controllability for fractional systems with control delays and give some of their important properties. Our main method consists of defining an attainable set, which allows us to prove exact and weak controllability. Moreover, the main results include not only those of controllability but also a powerful Hilbert uniqueness method, which allows us to solve the minimum energy optimal control problem. More precisely, an explicit control is obtained that drives the system from an initial given state to a desired regional state with minimum energy. Two examples are given to illustrate the obtained theoretical results.This research was funded by The Portuguese Foundation for Science and Technology
(FCT鈥擣unda莽茫o para a Ci锚ncia e a Tecnologia), grant number UIDB/04106/2020 (CIDMA).publishe
Minimum Energy Problem in the Sense of Caputo for Fractional Neutral Evolution Systems in Banach Spaces
We investigate a class of fractional neutral evolution equations on Banach
spaces involving Caputo derivatives. Main results establish conditions for the
controllability of the fractional-order system and conditions for existence of
a solution to an optimal control problem of minimum energy. The results are
proved with the help of fixed-point and semigroup theories.Comment: This is a preprint of a paper whose final and definite form is
published Open Access in 'Axioms' at [https://doi.org/10.3390/axioms11080379