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<p>In modern theory of control systems engineering, various problems of tracking motion using a&#xa0;controlled object play important role. The given motion (or the given parametric curve) serves as an ideal model to be achieved by means of an appropriate choice of object control. Note that in control theory there exist several concepts of “good” trajectory tracking. For example, one can aim to minimize a&#xa0;specific integral functional measuring the deviation of a&#xa0;fixed projection of the trajectory of the controlled object from the given parametric curve. In this work we consider the problem of asymptotic tracking of a&#xa0;given parametric curve in the Euclidean space <i>R</i><sup><i>k</i></sup> (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(k \geqslant 1\)</EquationSource> </InlineEquation>) by means of projection of the trajectory of a&#xa0;controlled object of a&#xa0;rather general type, whose motion occurs in the Euclidean space <i>R</i><sup>2</sup><sup><i>k</i></sup>. We obtain sufficient conditions when such tracking is achievable.</p>

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On a Problem of Asymptotic Tracking of a Given Curve

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • M. S. Nikolsky

摘要

In modern theory of control systems engineering, various problems of tracking motion using a controlled object play important role. The given motion (or the given parametric curve) serves as an ideal model to be achieved by means of an appropriate choice of object control. Note that in control theory there exist several concepts of “good” trajectory tracking. For example, one can aim to minimize a specific integral functional measuring the deviation of a fixed projection of the trajectory of the controlled object from the given parametric curve. In this work we consider the problem of asymptotic tracking of a given parametric curve in the Euclidean space Rk ( \(k \geqslant 1\) ) by means of projection of the trajectory of a controlled object of a rather general type, whose motion occurs in the Euclidean space R2k. We obtain sufficient conditions when such tracking is achievable.