Variational necessary conditions for optimal control problems

Volume 21, Issue 3, pp 186--191 http://dx.doi.org/10.22436/jmcs.021.03.02

Publication Date: April 22, 2020 Submission Date: February 14, 2020 Revision Date: March 03, 2020 Accteptance Date: March 13, 2020

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Authors

Maawiya Ould Sidi - RT-M2A Laboratory, Mathematics Department, College of Science, Jouf University, P. O. Box 2014, Sakaka, Saudi Arabia.

Abstract

In this work, we consider infinite spatiotemporal systems. We use a more regular control function to reach the desired target prescribed on the system domain. After presenting the existence results, we characterize the solution to our problem through variations method.

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Keywords

• Infinite dimensional systems
• bilinear systems
• optimal control problems

MSC

•  93C10
•  65K05
•  37M05

References

• [1] V. Ayalaa, E. Cruzb, W. Kliemannc, L. R. Laura-Guarachid, Controllability properties of bilinear systems in dimension 2, J. Math. Computer Sci., 16 (2016), 554--575
  • View Article
  • Google Scholar


• [2] S. Boulaaras, Existence and uniqueness for solutions of parabolic quasi-variational inequalities with impulse control and nonlinear source terms, J. Nonlinear Sci. Appl., 9 (2016), 568--583
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [3] M. E. Bradly, S. Lenhart, Bilinear optimal control of a Kirchhoff plate to a desired profile, Optimal Control Appl. Methods, 18 (1997), 217--226
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [4] M. E. Bradly, S. Lenhart, J. M. Yong, Bilinear Optimal control of the Velocity term in a Kirchhoff plate equation, J. Math. Anal. Appl., 238 (1999), 451--467
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


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


• [6] H. R. Joshi, Optimal Control of the Convective Velocity Coefficient in a Parabolic Problem, Proceedings of World Congress on Nonlinear Analysis, 63 (2005), 1383--1390
  • View Article
  • Google Scholar
  • MATH


• [7] B. Kafash, A. Delavarkhalafi, Restarted State Parameterization Method for Optimal Control Problems, J. Math. Comput. Sci., 14 (2015), 151--161
  • View Article
  • Google Scholar


• [8] S. Lenhart, Optimal control of a convective diffusive fluid problem, Math. Models Methods Appl. Sci., 5 (1995), 225--237
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


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


• [10] A. Pazy, Semigroup of linear operators and applications to partial differential equations, Springer-Verlag, New York (1983)
  • View Article
  • MathSciNet
  • Google Scholar


• [11] A. Zakeri, M. A. Abchouyeh, Solving an Elliptic Optimal Control Problem with BEM and FEM, J. Math. Computer Sci., 4 (2012), 448--455
  • View Article


• [12] E. Zerrik, M. Ould Sidi, An output controllability of bilinear distributed system, Int. Review Autom. Control, 3 (2010), 466--473
  • Google Scholar


• [13] E. Zerrik, M. Ould Sidi, Regional Controllability for Infinite Dimensional Distributed Bilinear Systems, Int. J. control, 84 (2011), 2108--2116
  • Google Scholar


• [14] E. Zerrik, M. Ould Sidi, Constrained regional control problem for distributed bilinear systems, IET Control Theory Appl., 7 (2013), 1914--1921
  • View Article
  • Google Scholar


• [15] 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
  • Google Scholar
  • MATH


• [16] 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