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<p>In this paper, we study the feedback control problem for a mathematical model describing the motion of a nonlinear viscous fluid with infinite memory along the trajectories of the velocity field. The existence of an optimal control that gives a minimum to a given bounded and lower semicontinuous quality functional is proved. The proof uses the approximation-topological approach, the theory of regular Lagrangian flows, and the theory of topological degree for multivalued vector fields.</p>

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THE PROBLEM OF EXISTENCE OF FEEDBACK CONTROL FOR ONE NONLINEAR VISCOUS FRACTIONAL VOIGT MODEL

  • 期刊论文

  • 发表日期：

    2025年7月1日

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  • A. V. Zvyagin,
  • E. I. Kostenko

摘要

In this paper, we study the feedback control problem for a mathematical model describing the motion of a nonlinear viscous fluid with infinite memory along the trajectories of the velocity field. The existence of an optimal control that gives a minimum to a given bounded and lower semicontinuous quality functional is proved. The proof uses the approximation-topological approach, the theory of regular Lagrangian flows, and the theory of topological degree for multivalued vector fields.