106
Views
10
CrossRef citations to date
0
Altmetric
Original Articles

Regional optimal control problem of a class of infinite-dimensional bi-linear systems

&
Pages 1495-1504 | Received 27 Oct 2015, Accepted 02 Jul 2016, Published online: 01 Sep 2016

References

  • Addou, A., & Benbrik, A. (2002). Existence and uniqueness of optimal control for a distributed parameter bilinear system. Journal of Dynamical and Control Systems, 8, 141–152.
  • Ball, J.M., Marsden, J.E., & Slemrod, M. (1982). Controllability for distributed bilinear systems. SIAM Journal on Control and Optimization, 20, 575–597.
  • Bradley, M.E., Lenhart, S., & Yong, J. (1999). Bilinear optimal control of the velocity term in a Kirchhoff plate equation. Journal of Mathematical Analysis and Applications, 2(238), 451–467.
  • Clérin, J.M. (2011). Well-posed state equations in bilinear control. Revue Roumaine de Mathématique Pures et Appliquées, 2(56), 115–136.
  • Clérin, J.M. (2012). Sensitivity analysis of a bilinear optimal control problem. Annales Mathématiques Blaise Pascal, 19, 177–196.
  • El Jai, A., Simon, M.S., Zerrik, E., Pritchard, A.J. (1995). Regional controllability of distributed systems. International Journal of Control, 62, 1351–1365.
  • Hermes, H. (1979). Local controllability of observables in finite and infinite dimensional nonlinear control systems. Applied Mathematics and Optimization, 5, 117–125.
  • Ito, K., & Kunisch, K. (2007). Optimal bilinear control of an abstract Schrôdinger equation. SIAM Journal on Control and Optimization, 46, 274–287.
  • Khapalov, A.Y. (2002). On bilinear controllability of the parabolic equation with the reaction diffusion term satisfying Newton's Law. Journal of Computational and Applied Mathematics, 21, 1–23.
  • Khapalov, A.Y. (2003). Controllability of the semilinear parabolic equation governed by a multiplicative control in the reaction term: a qualitative approach. SIAM Journal on Control and Optimization, 41, 1886–1990.
  • Lenhart, S. (1995). Optimal control of a convective-diffusive fluid problem. Mathematical Models and Methods in Applied Sciences, 5, 225–237.
  • Lions, J.L., & Magénes, E. (1968). Problèmes aux limites non homgènes et applications (Vols. 1). Paris: Dunod.
  • Mohler, R.R. (1973). Bilinear control processes. New York, NY and London: Academic Press.
  • Trentin, D., & Guyader, J.L. (1994). Vibration of a master plate with attached masses using modal sampling method. The Journal of the Acoustical Society of America, 96, 235–245.
  • Yi-Yuan, Y. (1996). Vibrations of elastic plates, New York, NY: Springer.
  • Zerrik, E. (2014). Regional quadratic control problem for distributed bilinear systems with bounded controls. International Journal of Control, 84, 2108–2116.
  • Zerrik, E., & Ould sidi, M. (2010). An output controllability of bilinear distributed system. International Review of Automatic Control, 3(5), 466.
  • Ztot, K., Zerrik, E., & Bourray, H. (2011). Regional control problem for distributed bilinear systems. International Journal of Applied Mathematics and Computer Science, 21, 499–508.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.