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Optimal Error Quantification and Robust Tracking under Unknown Upper Bounds on Uncertainties and Biased External Disturbance

Author

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  • Victor F. Sokolov

    (Institute of Physics and Mathematics, Federal Research Center Komi Science Center, Ural Branch, RAS, 167982 Syktyvkar, Russia)

Abstract

This paper addresses a problem of optimal error quantification in the framework of robust control theory in the 𝓁 1 setup. The upper bounds of biased external disturbance and the gains of coprime factor perturbations in a discrete-time linear time invariant SISO plant are assumed to be unknown. The computation of optimal data-consistent upper bounds under a known bias of external disturbance has been simplified to linear programming. This allows for the computation of optimal estimates in real-time and their application to achieve optimal robust steady-state tracking even when facing an unknown bias in the external disturbance. The presented results have been illustrated through computer simulations.

Suggested Citation

  • Victor F. Sokolov, 2024. "Optimal Error Quantification and Robust Tracking under Unknown Upper Bounds on Uncertainties and Biased External Disturbance," Mathematics, MDPI, vol. 12(2), pages 1-14, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:197-:d:1314661
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