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Universal Stabilisation System for Control Object Motion along the Optimal Trajectory

Author

Listed:
  • Askhat Diveev

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44, build. 2, Vavilova Str., Moscow 119333, Russia
    These authors contributed equally to this work.)

  • Elena Sofronova

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44, build. 2, Vavilova Str., Moscow 119333, Russia
    These authors contributed equally to this work.)

Abstract

An attempt to construct a universal stabilisation system that ensures the object motion along specified trajectory from certain class is presented. If such a stabilisation system is constructed, then only the problem of optimal control is solved, but for a model of the object, which includes a stabilisation system and a subsystem with a reference model for generating a specified trajectory. In this case, the desired control is the control in the reference model. Statement of complete optimal control problem includes two problems, optimal control problem and stabilisation system synthesis problem for motion along given trajectory in the state space. Numerical methods for solving these problems based on evolutionary computation and symbolic regression are described. It is shown that when solving the stabilisation system synthesis problem, it is possible to obtain a universal system that provides stabilisation of the object motion relative to any trajectory from a certain class. Therefore, it is advisable to formulate an optimal control problem for an object with a motion stabilisation system. A computational example of solving the problem for the spatial motion of a quadrocopter is given.

Suggested Citation

  • Askhat Diveev & Elena Sofronova, 2023. "Universal Stabilisation System for Control Object Motion along the Optimal Trajectory," Mathematics, MDPI, vol. 11(16), pages 1-20, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3556-:d:1219134
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    References listed on IDEAS

    as
    1. Mapopa Chipofya & Deok Jin Lee & Kil To Chong, 2015. "Trajectory Tracking and Stabilization of a Quadrotor Using Model Predictive Control of Laguerre Functions," Abstract and Applied Analysis, Hindawi, vol. 2015, pages 1-11, February.
    2. Francesco Marchetti & Edmondo Minisci, 2021. "Genetic Programming Guidance Control System for a Reentry Vehicle under Uncertainties," Mathematics, MDPI, vol. 9(16), pages 1-19, August.
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    Cited by:

    1. Askhat Diveev & Elena Sofronova & Nurbek Konyrbaev, 2024. "A Stabilisation System Synthesis for Motion along a Preset Trajectory and Its Solution by Symbolic Regression," Mathematics, MDPI, vol. 12(5), pages 1-14, February.
    2. Askhat Diveev & Elena Sofronova & Nurbek Konyrbaev & Oralbek Abdullayev, 2024. "Advanced Model with a Trajectory Tracking Stabilisation System and Feasible Solution of the Optimal Control Problem," Mathematics, MDPI, vol. 12(20), pages 1-20, October.

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