The Optimal Control Problem for Parabolic Equation with Nonlocal Boundary Conditions in Circular Sector

2015 ◽  
pp. 297-314 ◽  
Author(s):  
V. O. Kapustyan ◽  
O. A. Kapustian ◽  
O. V. Kapustyan ◽  
O. K. Mazur
Keyword(s):  
Optimal Control ◽  
Parabolic Equation ◽  
Optimal Control Problem ◽  
Boundary Conditions ◽  
Control Problem ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Circular Sector

scholarly journals SOLUTION TO THE OPTIMAL CONTROL PROBLEM BY SOURCES IN THE BOUNDARY CONDITIONS OF A HYPERBOLIC SYSTEM OF A NETWORK STRUCTURE

2021 ◽  
Vol 8 (1) ◽  
pp. 004-012
Author(s):  
Y. R. Ashrafova ◽  
◽  
S. R. Rasulova ◽  
◽  
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Conditions ◽  
Control Problem ◽  
Initial Conditions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Distributed Parameters ◽  
Long Duration ◽  
Internal Sources

The solution to the optimal control problem by power of external and internal sources acting on the multilink system in nonlocal boundary conditions is investigated. Each arc of the system is an object with distributed parameters, described by a differential equation of hyperbolic type and related only by boundary values, and in an arbitrary way. Due to the long duration of the object's functioning, the exact values of the initial conditions are not known, but a set of their possible values is given. Based on the results of additional measurements of the state of the process at the input or output ends of the arcs (which are not internal vertices), a target functional is constructed, for which minimization a formula for its gradient is obtained.

OPTIMAL CONTROL IN MODELS WITH CONDUCTIVE‐RADIATIVE HEAT TRANSFER

2003 ◽  
Vol 8 (1) ◽  
pp. 1-12 ◽  
Author(s):  
K. Birgelis
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Value Problem ◽  
Control Problem ◽  
Control Parameter ◽  
Elliptic Boundary ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Elliptic Boundary Value

In this paper an optimal control problem for the elliptic boundary value problem with nonlocal boundary conditions is considered. It is shown that the weak solutions of the boundary value problem depend smoothly on the control parameter and that the cost functional of the optimal control problem is Frechet differentiable with respect to the control parameter.

scholarly journals Asymptotic analysis of an optimal control problem for a viscous incompressible fluid with Navier slip boundary conditions

2021 ◽  
pp. 1-21
Author(s):  
Claudia Gariboldi ◽  
Takéo Takahashi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Boundary Conditions ◽  
Control Problem ◽  
Stokes System ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Slip ◽  
Slip Boundary ◽  
Navier Slip Boundary Conditions

We consider an optimal control problem for the Navier–Stokes system with Navier slip boundary conditions. We denote by α the friction coefficient and we analyze the asymptotic behavior of such a problem as α → ∞. More precisely, we prove that if we take an optimal control for each α, then there exists a sequence of optimal controls converging to an optimal control of the same optimal control problem for the Navier–Stokes system with the Dirichlet boundary condition. We also show the convergence of the corresponding direct and adjoint states.

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