198
Views
6
CrossRef citations to date
0
Altmetric
Research Article

Mild Solution and Approximate Controllability of Retarded Semilinear Systems with Control Delays and Nonlocal Conditions

&
Pages 721-737 | Received 25 Jan 2020, Accepted 07 May 2021, Published online: 26 May 2021

References

  • Kalman, R. E. (1960). Contributions to the theory of optimal control. Bol. Soc. Mate. Mexicana. 5(1):102–119.
  • Wang, L. (2009). Approximate controllability of integrodifferential equations with multiple delays. J. Optim. Theory Appl. 143(1):185–206. DOI: 10.1007/s10957-009-9545-0.
  • Naito, K. (1987). Controllability of semilinear control systems dominated by the linear part. SIAM J. Control Optim. 25(3):715–722. DOI: 10.1137/0325040.
  • Klamka, J. (2008). Stochastic controllability of systems with variable delay in control. Bull. Pol. Ac. Tech. 56(3):279–284.
  • Klamka, J. (2008). Stochastic controllability and minimum energy control of systems with multiple delays in control. Appl. Math. Comp. 206(2):704–715. DOI: 10.1016/j.amc.2008.08.059.
  • Davies, I., Jackreece, P. (2005). Controllability and null controllability of linear systems. J. Appl. Sci. Environ. Manag. 9:31–36.
  • Klamka, J. (2009). Constrained controllability of semilinear systems with delays. Nonlinear Dyn. 56(1–2):169–177. DOI: 10.1007/s11071-008-9389-4.
  • Mahmudov, N. I. (2018). Partial-approximate controllability of nonlocal evolution equations via approximating method. Appl. Math. Comp. 334:227–238. DOI: 10.1016/j.amc.2018.03.116.
  • Klamka, J. (1976). Controllability of linear systems with time-variable delays in control. Int. J. Control. 24(6):869–878. DOI: 10.1080/00207177608932867.
  • Kumar, S., Sukavanam, N. (2015). Controllability of semilinear systems with fixed delay in control. OpMath. 35(1):71–83. DOI: 10.7494/OpMath.2015.35.1.71.
  • Kumar, S., Tomar, N. K. (2018). Mild solution and controllability of second order nonlocal retarded semilinear systems. IMA J. Math. Control Inform. 37(1):39–49. DOI: 10.1093/imamci/dny037.
  • Haq, A., Sukavanam, N. (2020). Controllability of second-order nonlocal retarded semilinear systems with delay in control. Appl. Anal. 99(16):2741–2754. DOI: 10.1080/00036811.2019.1582031.
  • Chabrowski, J. (1984). On nonlocal problems for parabolic equations. Nagoya Math. J. 93:109–131. DOI: 10.1017/S0027763000020754.
  • Byszewski, L. (1991). Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem. J. Math. Anal. Appl. 162(2):494–505. DOI: 10.1016/0022-247X(91)90164-U.
  • Dubey, S. A., Bahuguna, D. (2009). Existence and regularity of solutions to nonlocal retarded differential equations. Appl. Math. Comp. 215(7):2413–2424. DOI: 10.1016/j.amc.2009.08.036.
  • Byszewski, L., Lakshmikantham, V. (1991). Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach Space. Appl. Anal. 40(1):11–19. DOI: 10.1080/00036819008839989.
  • Kumar, S., Sukavanam, N. (2014). Controllability of second order systems with nonlocal conditions in Banach spaces. Numer. Funct. Anal. Optim. 35(4):423–431. DOI: 10.1080/01630563.2013.814067.
  • Haq, A., Sukavanam, N. (2020). Partial approximate controllability of fractional systems with Riemann-Liouville derivatives and nonlocal conditions. Rend. Circ. Mat. Palermo. (2):1–16.
  • Tomar, N. K., Kumar, S. (2012). Approximate controllability of non local semilinear time-varying delay control systems. Nonlinear Dyn. Syst. Theory. 12(3):303–310.
  • Arora, U., Sukavanam, N. (2015). Approximate controllability of second order semilinear stochastic system with nonlocal conditions. Appl. Math. Comp. 258:111–119. DOI: 10.1016/j.amc.2015.01.118.
  • Klamka, J. (2008). Constrained controllability of semilinear systems with delayed controls. Bull. Pol. Acad. Sci. Tech. Sci. 56(4):333–337.
  • Klamka, J. (2004). Constrained controllability of semilinear systems with multiple delays in control. Bull. Pol. Acad. Sci. Tech. Sci. 52(1):25–30.
  • Klamka, J. (1977). On the controllability of linear systems with delays in the control. Int. J. Control. 25(6):875–883. DOI: 10.1080/00207177708922275.
  • Shen, L., Sun, J. (2013). Approximate controllability of abstract stochastic impulsive systems with multiple time-varying delays. Int. J. Robust Nonlinear Control. 23(8):827–838. DOI: 10.1002/rnc.2789.
  • Klamka, J. (2009). Stochastic controllability of systems with multiple delays in control. Int. J. Appl. Math. Comput. Sci. 19(1):39–47. DOI: 10.2478/v10006-009-0003-9.
  • Curtain, R. F., Zwart, H. (1995). An Introduction to Infinite Dimensional Linear Systems Theory, Texts in Applied Mathematics, Vol. 21, New York: Springer.

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.