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Computation of control for linear approximately controllable system using weighted Tikhonov regularization

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  • Katta, Ravinder
  • Reddy, G.D.
  • Sukavanam, N.

Abstract

Computing steering control for an approximately controllable linear system for a given target state is an ill-posed problem. We use a weighted Tikhonov regularization method and compute the regularized control. It is proved that the target state corresponding to the regularized control is close to the actual state to be attained. We also obtained error estimates and convergence rates involved in the regularization procedure using both the a priori and a posteriori parameter choice rule. Theory is substantiated with numerical experiments.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:317:y:2018:i:c:p:252-263
    DOI: 10.1016/j.amc.2017.08.012
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    References listed on IDEAS

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    1. 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.
    2. Rajan, M.P. & Reddy, G.D., 2015. "A variant of Tikhonov regularization for parabolic PDE with space derivative multiplied by a small parameter ∊," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 412-426.
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