A Notes on the Boundary Gradient Controllability for Hyperbolic Systems: Approaches and Simulations

Imad El Harraki; Ali Boutoulout

doi:10.15866/ireaco.v8i3.5220

A Notes on the Boundary Gradient Controllability for Hyperbolic Systems: Approaches and Simulations

Imad El Harraki⁽¹⁾, Ali Boutoulout^(2*)

^(*) Corresponding author

Authors' affiliations

DOI: https://doi.org/10.15866/ireaco.v8i3.5220

Abstract

In this paper, we treat the problem of the regional boundary exact controllability result of a flux for hyperbolic systems. We use two approaches; the first one gives an explicit expression of the optimal control to attain a desired gradient on a subregion part of the boundary ∂Ω. The second one uses the HUM approach by combining two controls and leads to a numerical approach. Finally, we will give an algorithm that we have programmed and tested successfully in an example.
Copyright © 2015 Praise Worthy Prize - All rights reserved.

Keywords

Hyperbolic Systems; Gradient Controllability; Direct Approach; HUM Approach

Full Text:

PDF

References

A. Boutoulout, H. Bourray and F. El Alaoui, Regional gradient observability for distribued semilinear parabolic systems, Journal of Dynamical and Control Systems, Vol. 18, No.2:259-179, 2012.
http://dx.doi.org/10.1007/s10883-012-9138-3

A. El Jaï, M. C. Simon, E. Zerrik, and A. J. Pritchard, Regional controllability of distributed parameter systems, International Journal of Control, Vol. 63, No.6:1351-1365, 1995.
http://dx.doi.org/10.1080/00207179508921603

A. El Jai and A.J. Prichard, Sensors and actuators in distributed systems analysis, Ellis Horwood series in applied mathematics, J. Wiley, 1988.

A. Kamal, A. Boutoulout, S. A. Ould Beinane, Regional Boundary Controllability of Semi-Linear Distributed Parabolic Systems, (2010) International Review of Automatic Control (IREACO), 3 (4), pp. 378-387.
http://dx.doi.org/10.4236/ica.2012.32017

A. Pazy, Semigroups of linear operators and applications to partial differential equations, Springer-Verlag, New-York, 1983.
http://dx.doi.org/10.1007/978-1-4612-5561-1

E. Zerrik and A. Boutoulout and A. Kamal, Regional gradient controllability of parabolic systems, Int. J. appl. Math and Comp. Sci, Vol. 9, No. 4: 767-787, 1999.

J. L. Lions, Contrôlabilité éxacte perturbation et stabilisation des systèmes distribués, Tome 1, Masson, 1988.
http://dx.doi.org/10.1007/bfb0007542

J. L. Lions, E. Magenes, Problèmes aux limites non homogènes et applications, Vol. 1 et 2. Dunod, 1968.
http://dx.doi.org/10.5802/aif.111

R. F. Curtain and H. Zwart, An introduction to infinite dimentional linear systems theory, Springer Verlag, NewYork, 1995.
http://dx.doi.org/10.1007/978-1-4612-4224-6

S. Avdonin, L. Pandolfi, Simultaneous temperature and flux controllability for heat equations with memory, Dipartimento di Matematica, Politecnico di Torino, (Quarterly of Applied Mathematics, 71, 339-368, 2013) (Quarterly of Applied Mathematics S0033-569X (2012)-versione elettronica).
http://dx.doi.org/10.1090/s0033-569x-2012-01287-7

W.McLean, Strongly Elliptic Systems and Boundary Integral Equations, Cambridge University Press, 2000.
http://dx.doi.org/10.1017/s0013091501244435

J. Bouyaghroumni, Contrôlabilité et observalité des systèmes hyperboliques : approche numerique, PhD theses. Perpignan., 1990.

E. Zerrik. Regional target control of the wave equation, International Journal of Systems Science, 2001.
http://dx.doi.org/10.1080/00207720110035264

E. Zerrik, A. Kamal, and A. Boutoulout. Regional flux target with minimum energy, IEE Proceedings -Control Theory and Applications, 2002.
http://dx.doi.org/10.1049/ip-cta:20020455

E. Zerrik. An Output Controllability Problem for Semilinear Distributed Hyperbolic Systems, International Journal of Applied Mathematics and Computer Science, 2007
http://dx.doi.org/10.2478/v10006-007-0035-y

E. Zerrik. Sensors and boundary state reconstruction of hyperbolic systems, International Journal of Applied Mathematics and Computer Science, 2010.
http://dx.doi.org/10.2478/v10006-010-0016-4

A.E Bashirov, N. Mahmudov, N. semi and H. Etikan. Patial controllability concepts, International journal of control, Vol 80 N1, pp 1-7, 2007.
http://dx.doi.org/10.1080/00207170600885489

Refbacks

There are currently no refbacks.

Username
Password
Remember me