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Optimal Control of Maximum Output Deviations of a Linear Time-Varying System on a Finite Horizon

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Abstract

The maximum output deviation of a linear time-varying system is defined as the worst-case measure of the maximum value of the output Euclidean norm over a finite horizon provided that the sum of the squared energy of an external disturbance and a quadratic form of the initial state is 1. Maximum deviation is characterized in terms of solutions to differential matrix equations or inequalities. A modified concept of the boundedness of the system on a finite horizon under an external and initial disturbances is introduced and its connection with the concept of maximum deviation is established. Necessary and sufficient conditions for the boundedness of the system on a finite horizon are obtained. It is demonstrated that optimal controllers (including the multiobjective ones that minimize the maximum deviations of several outputs) as well as controllers ensuring the boundedness of the system can be designed using linear matrix inequalities.

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Acknowledgements

This work was supported by the Russian Foundation for Basic Research, projects nos. 18-41-520002, 19-01-00289. We are grateful to B.T. Polyak for helpful discussions.

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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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Correspondence to D. V. Balandin.

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Russian Text © The Author(s), 2019, published in Avtomatika i Telemekhanika, 2019, No. 10, pp. 37–61.

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Balandin, D.V., Biryukov, R.S. & Kogan, M.M. Optimal Control of Maximum Output Deviations of a Linear Time-Varying System on a Finite Horizon. Autom Remote Control 80, 1783–1802 (2019). https://doi.org/10.1134/S0005117919100023

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