Feedback Optimal Control Problem for a Network Model     of Viscous Fluid Flows

Baranovskii, Evgenii S.

doi:10.1134/s0001434622070033

Cited by 17 publications

(5 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Remark 4. Another approach to the statement of boundary control problems for flow models is based on the use of boundary conditions for the dynamic pressure at permeable parts of the boundary of a flow region [35][36][37].…”

Section: Problem Formulation and The Main Resultsmentioning

confidence: 99%

Optimal Dirichlet Boundary Control for the Corotational Oldroyd Model

Baranovskii

Артемов

2023

Mathematics

View full text Add to dashboard Cite

In this article, we investigate an optimal control problem for the coupled system of partial differential equations describing the steady-state flow of a corotational-type Oldroyd fluid through a bounded 3D (or 2D) domain. The control function is included in Dirichlet boundary conditions for the velocity field; in other words, we consider a model of inflow–outflow control. The main result is a theorem that states sufficient conditions for the solvability of the corresponding optimization problem in the set of admissible weak solutions. Namely, we establish the existence of a weak solution that minimizes the cost functional under given constraints on controls and states.

show abstract

Section: Problem Formulation and The Main Resultsmentioning

confidence: 99%

Optimal Dirichlet Boundary Control for the Corotational Oldroyd Model

Baranovskii

Артемов

2023

Mathematics

View full text Add to dashboard Cite

show abstract

“…We have shown the existence of a solution in the time interval r0, T 1 s in Lemma 1. Let us now consider the energy estimate (17) with T bord ptq expressed in terms of the control commands…”

Section: Short-time Control Building Processmentioning

confidence: 99%

“…It also discusses the associated challenges, such as start-control, impulse-control and distributed-control laws, which have been studied for the Oseen and Navier-Stokes equations. Recently, global solution as well as an optimality system and a second-order sufficient optimality condition were obtained for the stationary two-dimensional Stokes equations [15,16], while an optimal controllability of a stationary two-dimensional non-Newtonian fluid in a pipeline network is studied in [17].…”

Section: Introductionmentioning

confidence: 99%

Boundary Feedback Stabilization of Two-Dimensional Shallow Water Equations with Viscosity Term

2022

View full text Add to dashboard Cite

This paper treats a water flow regularization problem by means of local boundary conditions for the two-dimensional viscous shallow water equations. Using an a-priori energy estimate of the perturbation state and the Faedo–Galerkin method, we build a stabilizing boundary feedback control law for the volumetric flow in a finite time that is prescribed by the solvability of the associated Cauchy problem. We iterate the same approach to build by cascade a stabilizing feedback control law for infinite time. Thanks to a positive arbitrary time-dependent stabilization function, the control law provides an exponential decay of the energy.

show abstract

“…The short time existence of a strong solution was proved for

\frac{7}{5}&lt;p\le 2

in the case of the periodic boundary in [6, 7], while for

\frac{5}{3}&lt;p&lt;2

in the case of whole space in [8]. Sufficient conditions for the existence of optimal boundary controls to non‐Newtonian flows with shear‐dependent viscosity were established in [9–11].…”

Section: Introductionmentioning

confidence: 99%