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Linear Quadratic Regulator: II. Robust Formulations

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Abstract

The classical linear quadratic regulation problem is considered in the robust formulations where the matrices of the system and/or initial conditions are not know precisely. Several approaches are proposed where the quadratic cost is minimized against the worst-case uncertainties. Finding such controllers is performed via reducing the matrix Riccati equation with uncertainty to a single linear matrix inequality. The properties of the solutions are discussed and the comparison with previously known approaches is performed.

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Acknowledgements

This work was supported in part by the Russian Foundation for Basic Research, project no. 18-08-00140.

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Authors and Affiliations

  1. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    M. V. Khlebnikov & P. S. Shcherbakov

  2. Institute for Systems Analysis, Russian Academy of Sciences, Moscow, Russia

    P. S. Shcherbakov

Authors
  1. M. V. Khlebnikov
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  2. P. S. Shcherbakov
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Correspondence to M. V. Khlebnikov.

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Russian Text © The Author(s), 2019, published in Avtomatika i Telemekhanika, 2019, No. 10, pp. 115–131.

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Khlebnikov, M.V., Shcherbakov, P.S. Linear Quadratic Regulator: II. Robust Formulations. Autom Remote Control 80, 1847–1860 (2019). https://doi.org/10.1134/S0005117919100060

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