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Robust Tracking as Constrained Optimization by Uncertain Dynamic Plant: Mirror Descent Method and ASG—Version of Integral Sliding Mode Control

Author

Listed:
  • Alexander Nazin

    (V. A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow 117997, Russia
    These authors contributed equally to this work.)

  • Hussain Alazki

    (Facultad de Ingeniería, Universidad Autónoma del Carmen (UNACAR), Playa del Carmen 24180, Mexico
    These authors contributed equally to this work.)

  • Alexander Poznyak

    (Automatic Control Department, Centro de Investigacion y Estudios Avanzados del Instituto Politecnico Nacional, Ciudad de Mexico 07360, Mexico
    These authors contributed equally to this work.)

Abstract

A class of controlled objects is considered, the dynamics of which are determined by a vector system of ordinary differential equations with a partially known right-hand side. It is presumed that the state variables and their velocities can be measured. Designing a robust tracking controller under some constraints to admissible state variables is the research goal. This construction, which extends the results for the average subgradient technique (ASG), and is an update of the subgradient descent technique (SDM) and integral sliding mode (ISM) approach, is realized by using the Legendre–Fenchel transform. A two-link robot manipulator with three revolute joints, powered by individual PMDC motors, is presented as an illustrative example of the suggested approach implementation.

Suggested Citation

  • Alexander Nazin & Hussain Alazki & Alexander Poznyak, 2023. "Robust Tracking as Constrained Optimization by Uncertain Dynamic Plant: Mirror Descent Method and ASG—Version of Integral Sliding Mode Control," Mathematics, MDPI, vol. 11(19), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4112-:d:1250268
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    References listed on IDEAS

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    1. A. Ferrara & V.I. Utkin, 2002. "Sliding Mode Optimization in Dynamic LTI Systems," Journal of Optimization Theory and Applications, Springer, vol. 115(3), pages 727-740, December.
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    Cited by:

    1. Patricio Borbolla-Burillo & David Sotelo & Michael Frye & Luis E. Garza-Castañón & Luis Juárez-Moreno & Carlos Sotelo, 2024. "Design and Real-Time Implementation of a Cascaded Model Predictive Control Architecture for Unmanned Aerial Vehicles," Mathematics, MDPI, vol. 12(5), pages 1-20, February.

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