Regional averaged control problems with minimum energy constrained by distributed parabolic systems

Volume 26, Issue 4, pp 349--356 http://dx.doi.org/10.22436/jmcs.026.04.03

Publication Date: December 08, 2021 Submission Date: November 12, 2021 Revision Date: November 22, 2021 Accteptance Date: November 23, 2021

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Authors

M. Ould Sidi - RT-M2A Laboratory, Mathematics Department, College of Science, Jouf University, P. O. Box: 2014, Sakaka, Saudi Arabia. R. Zine - School of Science and Engineering, Al Akhawayn University in Ifrane, Morocco. A. A. Mohamed - Department of Mathematics, College of Science and Humanities in Al-Aflaj, rince Sattam bin Abdulaziz University, Saudi Arabia.

Abstract

This paper study the regional average controllability problems governed by distributed parabolic systems. We establish the definition and characterization of a system which is regional averaged controllable. The averaged regional control problem with minimum energy is considered and solved using HUM (Hilbert uniqueness method). Thereafter, the case of regional gradient averaged controllability is treated.

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Keywords

• Distributed systems
• average controllability
• regional controllability
• gradient controllability
• minimum energy

MSC

•  93B40
•  93B52
•  49K99
•  49J99

References

• [1] H. Brezis, Analyse fonctionnelle, Masson, Paris (1983)
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [2] A. El Jai, A. J. Pritchard, Capteurs et actionneurs dans l'analyse des systeemes distribuees, Research in Applied Mathematics, Masson, Paris (1986)
  • Google Scholar


• [3] A. El Jai, M. C. Simon, E. Zerrik, A. J. Pritchard, Regional controllability of distributed parameter systems, Internat. J. Control, 62 (1995), 1351--1365
  • View Article
  • MathSciNet


• [4] J.-L. Lions, E. Magenes, Problèmes aux limites non homogènes et applications, Dunod, Paris (1968)
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] J. Loheac, E. Zuazua, Averaged controllability of parameter dependent conservative semigroups, J. Differential Equations, 262 (2017), 1540--1574
  • View Article
  • MathSciNet


• [6] Q. Lü, E. Zuazua, Averaged controllability for random evolution partial differential equations, J. Math. Pures Appl. (9), 105 (2016), 367--414
  • View Article
  • MathSciNet


• [7] M. Ould Sidi, S. A. Beinane, Regional gradient optimal control problem governed by a distributed bilinear systems, Telkomnika, 17 (2019), 1957--1965
  • View Article
  • Google Scholar


• [8] E. Zerrik, A. Boutoulout, A. Kamal, Regional Controllability of Parabolic systems, Int. J. Appl. Math. Comput. Sci., 9 (1999), 767--787
  • View Article
  • MathSciNet


• [9] E. Zerrik, A. Kamal, A. Boutoulout, Regional gradient controllability and actuators, Internat. J. Systems Sci., 33 (2002), 239--246
  • View Article
  • MathSciNet


• [10] E. Zerrik, A. Kamal, A. Boutoulout, Regional flux target with minimum energy, Control Theor. Appl., 149 (2002), 349--356
  • View Article
  • Google Scholar


• [11] R. Zine, Optimal control for a class of bilinear hyperbolic distributed systems, Far East J. Math. Sci., 102 (2017), 1761--1775
  • Google Scholar


• [12] R. Zine, M. Ould Sidi, Regional optimal control problem with minimum energy for a class of bilinear distributed systems, IMA J. Math. Control Inform., 35 (2018), 1187--1199
  • View Article
  • MathSciNet


• [13] R. Zine, M. Ould Sidi, Regional optimal control problem governed by distributed bilinear hyperbolic systems, Int. J. Control Autom. Syst., 16 (2018), 1060--1069
  • View Article
  • Google Scholar


• [14] E. Zuazua, Averaged control, Automatica J. IFAC, 50 (2014), 3077--3087
  • View Article
  • MathSciNet