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Stabilization of nonlinear discrete-time dynamic control systems with a parameter and state-dependent coefficients

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Abstract

A numerical-analytical algorithm for designing nonlinear stabilizing regulators for the class of nonlinear discrete-time control systems is proposed that significantly reduces computational costs. The resulting regulator is suboptimal with respect to the constructed quadratic functional with state-dependent coefficients. The conditions for the stability of the closed-loop system are established, and a stability result is stated. Numerical results are presented showing that the nonlinear regulator designed is superior to the linear one with respect to both nonlinear and standard time-invariant cost functionals. An example demonstrates that the closed-loop system is uniformly asymptotically stable.

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Authors and Affiliations

  1. Federal Research Center “Computer Science and Control,”, Russian Academy of Sciences, pr. 60-letiya Oktyabrya 9, Moscow, 117312, Russia

    S. V. Emel’yanov, Yu. E. Danik, M. G. Dmitriev & D. A. Makarov

Authors
  1. S. V. Emel’yanov
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  2. Yu. E. Danik
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  3. M. G. Dmitriev
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  4. D. A. Makarov
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Corresponding author

Correspondence to S. V. Emel’yanov.

Additional information

Original Russian Text © S.V. Emel’yanov, Yu.E. Danik, M.G. Dmitriev, D.A. Makarov, 2016, published in Doklady Akademii Nauk, 2016, Vol. 466, No. 3, pp. 282–284.

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Emel’yanov, S.V., Danik, Y.E., Dmitriev, M.G. et al. Stabilization of nonlinear discrete-time dynamic control systems with a parameter and state-dependent coefficients. Dokl. Math. 93, 121–123 (2016). https://doi.org/10.1134/S1064562416010142

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  • DOI: https://doi.org/10.1134/S1064562416010142

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