First-Order System Least-Squares Methods for an Optimal Control Problem by the Stokes Flow

2009 ◽  
Vol 47 (2) ◽  
pp. 1524-1545 ◽  
Author(s):  
Soorok Ryu ◽  
Hyung-Chun Lee ◽  
Sang Dong Kim
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Least Squares ◽  
Stokes Flow ◽  
Order System ◽  
First Order

scholarly journals Optimal Control Based on the Polynomial Least Squares Method

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Constantin Bota ◽  
Bogdan Cǎruntu ◽  
Mǎdǎlina Sofia Pașca ◽  
Marioara Lǎpǎdat
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Variational Problem ◽  
Least Squares ◽  
Least Squares Method ◽  
Lagrange Equation ◽  
Control Law

In this paper an approach for computing an optimal control law based on the Polynomial Least Squares Method (PLSM) is presented. The initial optimal control problem is reformulated as a variational problem whose corresponding Euler-Lagrange equation is solved by using PLSM. A couple of examples emphasize the accuracy of the method.

Solution for fractional distributed optimal control problem by hybrid meshless method

2016 ◽  
Vol 24 (11) ◽  
pp. 2149-2164 ◽  
Author(s):  
Majid Darehmiraki ◽  
Mohammad Hadi Farahi ◽  
Sohrab Effati
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Least Squares ◽  
Meshless Method ◽  
Basis Functions ◽  
Moving Least Squares ◽  
Distributed Optimal Control

We use a hybrid local meshless method to solve the distributed optimal control problem of a system governed by parabolic partial differential equations with Caputo fractional time derivatives of order α ∈ (0, 1]. The presented meshless method is based on the linear combination of moving least squares and radial basis functions in the same compact support, this method will change between interpolation and approximation. The aim of this paper is to solve the system of coupled fractional partial differential equations, with necessary and sufficient conditions, for fractional distributed optimal control problems using a combination of moving least squares and radial basis functions. To keep matters simple, the problem has been considered in the one-dimensional case, however the techniques can be employed for both the two- and three-dimensional cases. Several test problems are employed and results of numerical experiments are presented. The obtained results confirm the acceptable accuracy of the proposed method.

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 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.

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