The problem of existence of feedback control for one nonlinear viscous fractional Voigt model

A. V. Zvyagin, E. I. Kostenko

Voronezh State University, Voronezh, Russia

Abstract: 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.

Keywords: feedback control, optimal control, nonlinear viscous fluid, approximation-topological approach, regular Lagrangian flow, topological degree.

UDC: 517.977

DOI: 10.22363/2413-3639-2024-70-4-586-596