scholarly journals An Optimal Control Problem Governed by Nonlinear First Order Dynamic Equation on Time Scales

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Jian-Ping Sun ◽  
Qiu-Yan Ren ◽  
Ya-Hong Zhao
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Time Scales ◽  
Dynamic Equation ◽  
Optimal Solution ◽  
Control Policy ◽  
Controlled System ◽  
First Order ◽  
Nonlinear Controlled System

In this paper, we are concerned with a class of optimal control problem governed by nonlinear first order dynamic equation on time scales. By imposing some suitable conditions on the related functions, for any given control policy, we first obtain the existence of a unique solution for the nonlinear controlled system. Then, we study the existence of an optimal solution for the optimal control problem.

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 An optimal control problem related to a 3D-chemotaxis-Navier-Stokes model

2021 ◽  
Author(s):  
Juan López-Ríos ◽  
Élder J. Villamizar-Roa
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Solution ◽  
Strong Solutions ◽  
External Source ◽  
Navier Stokes ◽  
State Equations ◽  
Velocity Equation ◽  
Concentration Equation

In this paper, we study an optimal control problem associated to a 3D-chemotaxis-Navier-Stokes model. First we prove the existence of global weak solutions of the state equations with a linear reaction term on the chemical concentration equation, and an external source on the velocity equation, both acting as controls on the system. Second, we establish aregularity criterion to get global-in-time strong solutions. Finally, we prove the existence of an optimal solution, and we establish a first-order optimality condition.

scholarly journals Optimal bilinear control problem related to a chemo-repulsion system in 2D domains

2020 ◽  
Vol 26 ◽  
pp. 29 ◽  
Author(s):  
Francisco Guillén-González ◽  
Exequiel Mallea-Zepeda ◽  
María Ángeles Rodríguez-Bellido
Keyword(s):  
Optimal Control ◽  
Control Problem ◽  
Optimal Solution ◽  
Strong Solutions ◽  
Global Optimal Solution ◽  
Production Term ◽  
Bilinear Control ◽  
First Order ◽  
Global Optimal ◽  
Bilinear Control Problem

In this paper, we study a bilinear optimal control problem associated to a chemo-repulsion model with linear production term in a bidimensional domain. The existence, uniqueness and regularity of strong solutions of this model are deduced, proving the existence of a global optimal solution. Afterwards, we derive first-order optimality conditions by using a Lagrange multipliers theorem.

Optimal control of a hyperbolic system that describes Slutsky demand

2021 ◽  
pp. 58-59
Author(s):  
Olha Milchenko
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Hyperbolic System ◽  
Method Of Characteristics ◽  
Social Processes ◽  
Computational Algorithms ◽  
Initial Condition ◽  
Linear Optimal Control ◽  
First Order

A non-linear optimal control problem for a hyperbolic system of first order equations on a line in the case of degeneracy of the initial condition line is considered. This problem describes many natural, economic and social processes, in particular, the optimality of the Slutsky demand, the theory of bio-population, etc. The research is based on the method of characteristics and the use of nonstandard variations of the increment of target functional, which leads to the construction of efficient computational algorithms.

scholarly journals High-order homogenization in optimal control by the Bloch wave method

2021 ◽  
Author(s):  
Agnes Lamacz-Keymling ◽  
Irwin Yousept
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Solution ◽  
Periodic Coefficient ◽  
State Equation ◽  
Bloch Wave ◽  
High Order ◽  
Effective Control ◽  
Linear Quadratic

This article examines a linear-quadratic elliptic optimal control problem in which the cost functional and the state equation involve a highly oscillatory periodic coefficient $A^\eps$. The small parameter $\eps>0$ denotes the periodicity length. We propose a high-order effective control problem with constant coefficients that provides an approximation of the original one with error $O(\eps^M)$, where $M\in\N$ is as large as one likes. Our analysis relies on a Bloch wave expansion of the optimal solution and is performed in two steps. In the first step, we expand the lowest Bloch eigenvalue in a Taylor series to obtain a high-order effective optimal control problem. In the second step, the original and the effective problem are rewritten in terms of the Bloch and the Fourier transform, respectively. This allows for a direct comparison of the optimal control problems via the corresponding variational inequalities, leading to our main theoretical result on the high-oder approximation.

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