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Symbolic Regulator Sets for a Weakly Nonlinear Discrete Control System with a Small Step

Author

Listed:
  • Yulia Danik

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 119333 Mocow, Russia)

  • Mikhail Dmitriev

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 119333 Mocow, Russia)

Abstract

For a class of discrete weakly nonlinear state-dependent coefficient (SDC) control systems, a suboptimal synthesis is constructed over a finite interval with a large number of steps. A one-point matrix Padé approximation ( PA ) of the solution of the initial problem for the discrete matrix Riccati equation is constructed based on the state-dependent Riccati equation (SDRE) approach and the asymptotics by the small-step of the boundary layer functions method. The symmetric gain coefficients matrix for Padé control synthesis is constructed based on the one-point PA . As a result, the parametric closed-loop control is obtained. The results of numerical experiments illustrate, in particular, the improved extrapolation properties of the constructed regulator, which makes the algorithm applicable in control systems for a wider range of parameter variation.

Suggested Citation

  • Yulia Danik & Mikhail Dmitriev, 2022. "Symbolic Regulator Sets for a Weakly Nonlinear Discrete Control System with a Small Step," Mathematics, MDPI, vol. 10(3), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:487-:d:741004
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    Citations

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    Cited by:

    1. Quanxin Zhu, 2022. "Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering," Mathematics, MDPI, vol. 10(24), pages 1-2, December.
    2. Peng Ji & Chenglong Li & Fengying Ma, 2022. "Sliding Mode Control of Manipulator Based on Improved Reaching Law and Sliding Surface," Mathematics, MDPI, vol. 10(11), pages 1-21, June.

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