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Abstract <p> A controllability criterion for a partial differential system with a small parametermultiplying the second derivative is obtained. The equivalence of this criterion to the Kalmancriterion is proved. The control and state functions are constructed explicitly, and the solution ofthe limit problem is found in closed form. The problem of constructing a control generatinga boundary layer phenomenon near two boundaries of a rectangular domain is solved.</p>

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Solution of a Control Problem for a Singularly Perturbed Dynamical System with Partial Derivatives

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • E. V. Raetskaya

摘要

Abstract

A controllability criterion for a partial differential system with a small parametermultiplying the second derivative is obtained. The equivalence of this criterion to the Kalmancriterion is proved. The control and state functions are constructed explicitly, and the solution ofthe limit problem is found in closed form. The problem of constructing a control generatinga boundary layer phenomenon near two boundaries of a rectangular domain is solved.