299 research outputs found
Regional gradient controllability of ultra-slow diffusions involving the Hadamard-Caputo time fractional derivative
This paper investigates the regional gradient controllability for ultra-slow
diffusion processes governed by the time fractional diffusion systems with a
Hadamard-Caputo time fractional derivative. Some necessary and sufficient
conditions on regional gradient exact and approximate controllability are first
given and proved in detail. Secondly, we propose an approach on how to
calculate the minimum number of strategic actuators. Moreover, the
existence, uniqueness and the concrete form of the optimal controller for the
system under consideration are presented by employing the Hilbert Uniqueness
Method (HUM) among all the admissible ones. Finally, we illustrate our results
by an interesting example.Comment: 16 page
Control theory for nonlinear fractional dispersive systems
We consider a terminal control problem for processes governed by a nonlinear
system of fractional ODEs. In order to show existence of the control, we first
consider the linear counterpart of the system and reprove a number of classical
theorems in the fractional setting (representation of the solution through the
Gramian type matrix, Kalman's principle, equivalence of the controllability and
observability). We are then in the position to use a fixed point theorem
approach and various techniques from the fractional calculus theory to get the
desired result
Control in moving interfaces and deep learning
Tesis Doctoral inédita leÃda en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Matemáticas. Fecha de Lectura: 14-05-2021This thesis has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.765579-ConFlex
Controllability of the one-dimensional fractional heat equation under positivity constraints
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Communications on Pure and Applied Analysis following peer review. The definitive publisher-authenticated version Biccari, U., Warma, M., & Zuazua, E. (2020). Controllability of the one-dimensional fractional heat equation under positivity constraints. Communications on Pure & Applied Analysis, 19(4), 1949-1978.
is available online at https://www.aimsciences.org/article/doi/10.3934/cpaa.2020086In this paper, we analyze the controllability properties under positivity constraints on the control or the state of a one-dimensional heat equation involving the fractional Laplacian (−dx2)s (0 < s < 1) on the interval (−1, 1). We prove the existence of a minimal (strictly positive) time Tmin such that the fractional heat dynamics can be controlled from any initial datum in L2(−1, 1) to a positive trajectory through the action of a positive control, when s > 1/2. Moreover, we show that in this minimal time constrained controllability is achieved by means of a control that belongs to a certain space of Radon measures. We also give some numerical simulations that confirm our theoretical resultsThis project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement NO. 694126-DyCon). The work of the three authors is partially supported by the Air Force Office of Scientific Research under Award NO: FA9550-18-1-0242. The work of the first and of the third author was partially supported by the Grant MTM2017-92996-C2-1-R COSNET of MINECO (Spain) and by the ELKARTEK project KK-2018/00083 ROAD2DC of the Basque Government. The work of the third author was partially supported by the Alexander von Humboldt-Professorship program, the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement NO. 765579-ConFlex, and by the Grant ICON-ANR-16-ACHN-0014 of the French AN
- …