scholarly journals Superconvergence for General Convex Optimal Control Problems Governed by Semilinear Parabolic Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Yongquan Dai ◽  
Yanping Chen
Keyword(s):  
Optimal Control ◽  
Parabolic Equations ◽  
Optimal Control Problems ◽  
Control Variable ◽  
The State ◽  
Control Problems ◽  
Element Approximation ◽  
Semilinear Parabolic Equations ◽  
State Variables ◽  
Semilinear Parabolic

We will investigate the superconvergence for the semidiscrete finite element approximation of distributed convex optimal control problems governed by semilinear parabolic equations. The state and costate are approximated by the piecewise linear functions and the control is approximated by piecewise constant functions. We present the superconvergence analysis for both the control variable and the state variables.

Superconvergence of Mixed Methods for Optimal Control Problems Governed by Parabolic Equations

2011 ◽  
Vol 3 (4) ◽  
pp. 401-419 ◽  
Author(s):  
Xiaoqing Xing ◽  
Yanping Chen
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Parabolic Equations ◽  
Optimal Control Problems ◽  
Mixed Finite Element ◽  
Control Variable ◽  
The State ◽  
Piecewise Constant Function ◽  
Control Problems ◽  
Element Approximation

AbstractIn this paper, we investigate the superconvergence results for optimal control problems governed by parabolic equations with semidiscrete mixed finite element approximation. We use the lowest order mixed finite element spaces to discrete the state and costate variables while use piecewise constant function to discrete the control variable. Superconvergence estimates for both the state variable and its gradient variable are obtained.

scholarly journals Existence of the Optimal Control for Stochastic Boundary Control Problems Governed by Semilinear Parabolic Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Weifeng Wang ◽  
Baobin Wang
Keyword(s):  
Boundary Condition ◽  
Optimal Control ◽  
Parabolic Equations ◽  
Control Variable ◽  
Control Problems ◽  
Semilinear Parabolic Equation ◽  
Semilinear Parabolic Equations ◽  
Boundary Control Problems ◽  
Semilinear Parabolic ◽  
Stochastic Boundary

We study an optimal control problem governed by a semilinear parabolic equation, whose control variable is contained only in the boundary condition. An existence theorem for the optimal control is obtained.

Error Estimates of Mixed Methods for Optimal Control Problems Governed by General Elliptic Equations

2016 ◽  
Vol 8 (6) ◽  
pp. 1050-1071 ◽  
Author(s):  
Tianliang Hou ◽  
Li Li
Keyword(s):  
Optimal Control ◽  
Finite Element ◽  
Error Estimates ◽  
Elliptic Equations ◽  
Optimal Control Problems ◽  
Mixed Finite Element ◽  
Control Variable ◽  
The State ◽  
Control Problems ◽  
General Elliptic

AbstractIn this paper, we investigate the error estimates of mixed finite element methods for optimal control problems governed by general elliptic equations. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control variable is approximated by piecewise constant functions. We derive L2 and H–1-error estimates both for the control variable and the state variables. Finally, a numerical example is given to demonstrate the theoretical results.

scholarly journals A numerical method for solving a class of fractional optimal control problems using Boubaker polynomial expansion scheme

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4485-4502 ◽  
Author(s):  
N. Singha ◽  
C. Nahak
Keyword(s):  
Optimal Control ◽  
Performance Index ◽  
Numerical Scheme ◽  
Optimal Control Problems ◽  
Control Variable ◽  
The State ◽  
Polynomial Expansion ◽  
Control Problems ◽  
Fractional Optimal Control ◽  
Fractional Optimal Control Problems

We construct a numerical scheme for solving a class of fractional optimal control problems by employing Boubaker polynomials. In the proposed scheme, the state and control variables are approximated by practicingNth-order Boubaker polynomial expansion. With these approximations, the given performance index is transformed to a function of N + 1 unknowns. The objective of the present formulation is to convert a fractional optimal control problem with quadratic performance index into an equivalent quadratic programming problem with linear equality constraints. Thus, the latter problem can be handled efficiently in comparison to the original problem. We solve several examples to exhibit the applicability and working mechanism of the presented numerical scheme. Graphical plots are provided to monitor the nature of the state, control variable and the absolute error function. All the numerical computations and graphical representations have been executed with the help of Mathematica software.

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