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Iterative design of robust controllers under unknown bounded perturbation norms

  • Adaptive and Robust Systems
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Abstract

A suboptimal robust controller for a multidimensional linear stationary nominal system with output- and control-operator perturbations and a bounded external perturbation is designed. Perturbation norms (weights) are assumed to be unknown and estimated from measurement data. The quality index of the closed-loop control system is taken to be the worst ℓ∞-norm for the output of the system in the class of admissible perturbations. The quality index for systems in the class of linear stationary stabilizing controllers is a fractional linear function of induced norms of transfer matrices of the closed-loop system and perturbation norms. The classical design of suboptimal robust controllers under known perturbation norms is reduced to a standard ℓ1-optimization problem, and optimal estimation of unknown perturbation norms is reduced to a linear programming problem. Therefore, the iterative sequential method of controller design and perturbation norm estimation is used as a heuristic method for designing suboptimal robust controllers under unknown perturbation norms. Modeling results corroborate the effectiveness of this method.

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Authors and Affiliations

  1. Department of Mathematics, Scientific Center, Ural Branch, Russian Academy of Sciences, Syktyvkar, Russia

    V. F. Sokolov

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  1. V. F. Sokolov
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Translated from Avtomatika i Telemekhanika, No. 4, 2005, pp. 110–126.

Original Russian Text Copyright © 2005 by Sokolov.

This work was supported by the Russian Foundation for Basic Research, project no. 02-01-00474.

This paper was recommended for publication by A.P. Kurdyukov, a member of the Editorial Board

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Sokolov, V.F. Iterative design of robust controllers under unknown bounded perturbation norms. Autom Remote Control 66, 606–619 (2005). https://doi.org/10.1007/s10513-005-0104-3

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  • DOI: https://doi.org/10.1007/s10513-005-0104-3

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