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Minimax Control of Deviations for the Outputs of a Linear Discrete Time-Varying System

  • Linear Systems
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Abstract

It is demonstrated how to design optimal digital controllers on a finite horizon for the linear time-varying objects with uncertain initial conditions and external disturbances. The square of an optimality criterion, called the maximum output deviation, represents the exact guaranteed maximum value of the squared Euclidean norm of the system output normalized by the sum of the squared Euclidean norms of disturbances and a quadratic form of the initial state of a system. The maximum output deviations and the worst-case disturbances and/or initial conditions causing them, as well as the minimax controllers (including the multiobjective ones that minimize the maximum deviations of several outputs) are calculated as solutions to a semidefinite programming problem. The necessary and sufficient conditions for the finite-time stability and boundedness of a system are established; they can be used for controller design.

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Acknowledgments

This work was supported by the Russian Foundation for Basic Research, projects nos. 18-41-520002, 19-01-00289.

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Authors and Affiliations

  1. Lobachevsky Nizhny Novgorod State University, Nizhny Novgorod, Russia

    D. V. Balandin

  2. Nizhny Novgorod State University of Architecture and Civil Engineering, Nizhny Novgorod, Russia

    R. S. Biryukov & M. M. Kogan

Authors
  1. D. V. Balandin
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  2. R. S. Biryukov
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  3. M. M. Kogan
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Corresponding authors

Correspondence to D. V. Balandin, R. S. Biryukov or M. M. Kogan.

Additional information

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

Russian Text © The Author(s), 2019, published in Avtomatika i Telemekhanika, 2019, No. 12, pp. 3–23.

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Balandin, D.V., Biryukov, R.S. & Kogan, M.M. Minimax Control of Deviations for the Outputs of a Linear Discrete Time-Varying System. Autom Remote Control 80, 2091–2107 (2019). https://doi.org/10.1134/S0005117919120014

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  • DOI: https://doi.org/10.1134/S0005117919120014

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