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Abstract <p> In the theory of optimal control, an important role is played by the attainable set of the controlled object <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(D(T)\)</EquationSource> </InlineEquation> at a given time <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(T\)</EquationSource> </InlineEquation>. For example, this set is useful in studying the dynamical possibilities of the controlled object. We study the nature of dependence of the attainable set of a linear non-stationary controlled object on disturbances of its dynamic characteristics. We establish constructive sufficient conditions of a general form that guarantee that the change of the attainable set, in the Hausdorff metric, is small if the changes of dynamic characteristics of a linear non-stationary controlled object are small in a certain sense. </p>

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On the Dependence of the Attainable Set of Linear Controlled Objects on Disturbances

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • M. S. Nikol’skii

摘要

Abstract

In the theory of optimal control, an important role is played by the attainable set of the controlled object \(D(T)\) at a given time \(T\) . For example, this set is useful in studying the dynamical possibilities of the controlled object. We study the nature of dependence of the attainable set of a linear non-stationary controlled object on disturbances of its dynamic characteristics. We establish constructive sufficient conditions of a general form that guarantee that the change of the attainable set, in the Hausdorff metric, is small if the changes of dynamic characteristics of a linear non-stationary controlled object are small in a certain sense.