Existence of a solution to a system of equations in variations in an optimal control problem

2021 ◽  
Vol 24 (1) ◽  
pp. 48-66
Author(s):  
K. S. Musabekov
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
System Of Equations ◽  
Existence Of A Solution

scholarly journals Optimal controllability for scalar conservation laws with convex flux

2014 ◽  
Vol 11 (03) ◽  
pp. 477-491 ◽  
Author(s):  
Adimurthi ◽  
Shyam Sundar Ghoshal ◽  
G. D. Veerappa Gowda
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Conservation Laws ◽  
Linear Problem ◽  
Optimal Solution ◽  
Scalar Conservation Laws ◽  
Existence Of A Solution ◽  
New Strategy ◽  
Scalar Conservation

The optimal control problem for Burgers equation was first considered by Castro, Palacios and Zuazua. They proved the existence of a solution and proposed a numerical scheme to capture an optimal solution via the method of "alternate decent direction". In this paper, we introduce a new strategy for the optimal control problem for scalar conservation laws with convex flux. We propose a new cost function and by the Lax–Oleinik explicit formula for entropy solutions, the nonlinear problem is converted to a linear problem. Exploiting this property, we prove the existence of an optimal solution and, by a backward construction, we give an algorithm to capture an optimal solution.

scholarly journals On the Dynamics of Controlled Magnetohydrodynamic Systems

2008 ◽  
Vol 13 (3) ◽  
pp. 351-377 ◽  
Author(s):  
S. S. Ravindran
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Solution ◽  
Mhd Equations ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Existence Of A Solution ◽  
Decay Properties ◽  
Long Time

In this paper we study the long time behavior of solutions for an optimal control problem associated with the viscous incompressible electrically conducting fluid modeled by the magnetohydrodynamic (MHD) equations in a bounded two dimensional domain through the adjustment of distributed controls. We first construct a quasi-optimal solution for the MHD systems which possesses exponential decay in time. We then derive some preliminary estimates for the long-time behavior of all admissible solutions of the MHD systems. Next we prove the existence of a solution for the optimal control problem for both finite and infinite time intervals. Finally, we establish the long-time decay properties of the solutions for the optimal control problem.

scholarly journals Nonlinear Fuzzy Differential Equation with Time Delay and Optimal Control Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Wichai Witayakiattilerd
Keyword(s):  
Differential Equation ◽  
Optimal Control ◽  
Time Delay ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Existence And Uniqueness ◽  
Fuzzy Differential Equation ◽  
Initial Value ◽  
Existence Of A Solution ◽  
Delay Function

The existence and uniqueness of a mild solution to nonlinear fuzzy differential equation constrained by initial value were proven. Initial value constraint was then replaced by delay function constraint and the existence of a solution to this type of problem was also proven. Furthermore, the existence of a solution to optimal control problem of the latter type of equation was proven.

scholarly journals Optimal location of a rigid inclusion in equilibrium problems for inhomogeneous Kirchhoff–Love plates with a crack

2019 ◽  
Vol 24 (12) ◽  
pp. 3743-3752 ◽  
Author(s):  
Nyurgun Lazarev ◽  
Hiromichi Itou
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Rigid Inclusion ◽  
Equilibrium Problems ◽  
Location Parameter ◽  
Continuous Functional ◽  
Existence Of A Solution ◽  
Crack Faces ◽  
Variational Statement

A non-linear model describing the equilibrium of a cracked plate with a volume rigid inclusion is studied. We consider a variational statement for the Kirchhoff–Love plate satisfying the Signorini-type non-penetration condition on the crack faces. For a family of problems, we study the dependence of their solutions on the location of the inclusion. We formulate an optimal control problem with a cost functional defined by an arbitrary continuous functional on a suitable Sobolev space. For this problem, the location parameter of the inclusion serves as a control parameter. We prove continuous dependence of the solutions with respect to the location parameter and the existence of a solution of the optimal control problem.

REDUCED MODEL OF PLASMA DISCHARGE CONTROL IN TOKAMAK WITH IRON CORE

2020 ◽  
Vol 7 (3) ◽  
pp. 11-22
Author(s):  
VALERY ANDREEV ◽  
◽  
ALEXANDER POPOV
Keyword(s):  
Optimal Control ◽  
Inverse Problem ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Nonlinear Behavior ◽  
Plasma Discharge ◽  
Reduced Model ◽  
Iron Core ◽  
Power Sources ◽  
Real Power

A reduced model has been developed to describe the time evolution of a discharge in an iron core tokamak, taking into account the nonlinear behavior of the ferromagnetic during the discharge. The calculation of the discharge scenario and program regime in the tokamak is formulated as an inverse problem - the optimal control problem. The methods for solving the problem are compared and the analysis of the correctness and stability of the control problem is carried out. A model of “quasi-optimal” control is proposed, which allows one to take into account real power sources. The discharge scenarios are calculated for the T-15 tokamak with an iron core.

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