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Abstract <p>The problem of controlling the <i>k</i>th derivative of an object state under a linear state constraint, where <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(k\)</EquationSource> <!--ComMat2570151Zhukova-m1--> </InlineEquation> is an arbitrary natural number, is studied. According to the existing terminology in literature, this is a so-called state-constrained control problem of order <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(k\)</EquationSource> <!--ComMat2570151Zhukova-m2--> </InlineEquation> (the term “of depth <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(k\)</EquationSource> <!--ComMat2570151Zhukova-m3--> </InlineEquation>” is also used). This paper applies Pontryagin’s maximum principle to the problem under study and conducts a theoretical analysis of the resulting optimality conditions. Based on this analysis, a computational scheme for finding extremals is proposed.</p>

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Calculation of Extremals in an Optimal Control Problem with a Higher-Order State Constraint

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • A. A. Zhukova,
  • D. Yu. Karamzin

摘要

Abstract

The problem of controlling the kth derivative of an object state under a linear state constraint, where \(k\) is an arbitrary natural number, is studied. According to the existing terminology in literature, this is a so-called state-constrained control problem of order \(k\) (the term “of depth \(k\) ” is also used). This paper applies Pontryagin’s maximum principle to the problem under study and conducts a theoretical analysis of the resulting optimality conditions. Based on this analysis, a computational scheme for finding extremals is proposed.