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Controllability of Nonlinear Systems in Banach Spaces: A Survey

Author

Listed:
  • K. Balachandran

    (Bharathiar University)

  • J.P. Dauer

    (University of Tennessee at Chattanooga)

Abstract

This paper presents a survey on research using fixed-point theorems and semigroup theory to study the controllability of nonlinear systems and functional integrodifferential systems in Banach spaces. Also discussed is the use of this technique in K-controllability and boundary controllability problems for nonlinear systems and integrodifferential systems in abstract spaces.

Suggested Citation

  • K. Balachandran & J.P. Dauer, 2002. "Controllability of Nonlinear Systems in Banach Spaces: A Survey," Journal of Optimization Theory and Applications, Springer, vol. 115(1), pages 7-28, October.
    • Handle: RePEc:spr:joptap:v:115:y:2002:i:1:d:10.1023_a:1019668728098
    DOI: 10.1023/A:1019668728098
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    References listed on IDEAS

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    1. W. M. Bian, 1999. "Controllability of Nonlinear Evolution Systems with Preassigned Responses," Journal of Optimization Theory and Applications, Springer, vol. 100(2), pages 265-285, February.
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    Cited by:

    1. Dimplekumar Chalishajar & Annamalai Anguraj & Kandasamy Malar & Kulandhivel Karthikeyan, 2016. "A Study of Controllability of Impulsive Neutral Evolution Integro-Differential Equations with State-Dependent Delay in Banach Spaces," Mathematics, MDPI, vol. 4(4), pages 1-16, October.
    2. Jerzy Klamka, 2020. "Controllability of Semilinear Systems with Multiple Variable Delays in Control," Mathematics, MDPI, vol. 8(11), pages 1-9, November.
    3. Vadivoo, B.Sundara & Raja, R. & Seadawy, R. Aly & Rajchakit, G., 2019. "Nonlinear integro-differential equations with small unknown parameters: A controllability analysis problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 15-26.
    4. Chang, Yong-Kui & Anguraj, A. & Mallika Arjunan, M., 2009. "Controllability of impulsive neutral functional differential inclusions with infinite delay in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1864-1876.
    5. Mouffak Benchohra & Fatima Bouazzaoui & Erdal Karapinar & Abdelkrim Salim, 2022. "Controllability of Second Order Functional Random Differential Equations with Delay," Mathematics, MDPI, vol. 10(7), pages 1-16, March.
    6. B. Radhakrishnan & K. Balachandran, 2012. "Controllability of Neutral Evolution Integrodifferential Systems with State Dependent Delay," Journal of Optimization Theory and Applications, Springer, vol. 153(1), pages 85-97, April.
    7. G. Arthi & K. Balachandran, 2012. "Controllability of Damped Second-Order Impulsive Neutral Functional Differential Systems with Infinite Delay," Journal of Optimization Theory and Applications, Springer, vol. 152(3), pages 799-813, March.
    8. Lizzy, R. Mabel & Balachandran, Krishnan & Trujillo, Juan J., 2017. "Controllability of nonlinear stochastic fractional neutral systems with multiple time varying delays in control," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 162-167.
    9. D. Tamizharasan & K. Karthikeyan, 2021. "Controllability results for fractional integrodifferential systems with boundary conditions," Indian Journal of Pure and Applied Mathematics, Springer, vol. 52(1), pages 39-45, March.
    10. Adisorn Doodee & Anusorn Chonwerayuth, 2022. "Controllability and Hyers-Ulam Stability of Impulsive Integro-differential Equations in Banach Spaces via Iterative Methods," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 14(4), pages 1-85, November.
    11. Katta, Ravinder & Reddy, G.D. & Sukavanam, N., 2018. "Computation of control for linear approximately controllable system using weighted Tikhonov regularization," Applied Mathematics and Computation, Elsevier, vol. 317(C), pages 252-263.
    12. L. W. Wang, 2009. "Approximate Controllability for Integrodifferential Equations with Multiple Delays," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 185-206, October.
    13. Chang, Yong-Kui, 2007. "Controllability of impulsive functional differential systems with infinite delay in Banach spaces," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1601-1609.
    14. Agata Grudzka & Krzysztof Rykaczewski, 2015. "On Approximate Controllability of Functional Impulsive Evolution Inclusions in a Hilbert Space," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 414-439, August.

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