Optimal Control Problem for Cahn–Hilliard Equations with State Constraint

2014 ◽  
Vol 21 (2) ◽  
pp. 257-272 ◽  
Author(s):  
Jiashan Zheng ◽  
Yifu Wang
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
State Constraint

scholarly journals Spectral Galerkin Approximation of Space Fractional Optimal Control Problem with Integral State Constraint

2021 ◽  
Vol 5 (3) ◽  
pp. 102
Author(s):  
Fangyuan Wang ◽  
Xiaodi Li ◽  
Zhaojie Zhou
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Jacobi Polynomials ◽  
A Priori ◽  
Galerkin Approximation ◽  
State Constraint ◽  
Diffusion Reaction ◽  
Lagrangian Multiplier ◽  
Adjoint State

In this paper spectral Galerkin approximation of optimal control problem governed by fractional advection diffusion reaction equation with integral state constraint is investigated. First order optimal condition of the control problem is discussed. Weighted Jacobi polynomials are used to approximate the state and adjoint state. A priori error estimates for control, state, adjoint state and Lagrangian multiplier are derived. Numerical experiment is carried out to illustrate the theoretical findings.

scholarly journals Optimal Control of Pseudoparabolic Variational Inequalities Involving State Constraint

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Youjun Xu ◽  
Shu Zhou
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Variational Inequalities ◽  
Control Problem ◽  
Control Process ◽  
State Constraint ◽  
Necessary Condition ◽  
Necessary Condition Of Optimality

We establish the necessary condition of optimality for optimal control problem governed by some pseudoparabolic differential equations involving monotone graphs. Some approximating control process and examples are given.

scholarly journals Optimal Control for the Thin Film Equation: Convergence of a Multi-Parameter Approach to Track State Constraints Avoiding Degeneracies

2016 ◽  
Vol 16 (4) ◽  
pp. 685-702
Author(s):  
Markus Klein ◽  
Andreas Prohl
Keyword(s):  
Thin Film ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
State Constraints ◽  
Necessary Optimality Conditions ◽  
State Constraint ◽  
The State ◽  
Well Posedness ◽  
Thin Film Equation

AbstractWe consider an optimal control problem subject to the thin-film equation. The PDE constraint lacks well-posedness for general right-hand sides due to possible degeneracies; state constraints are used to circumvent this problematic issue and to ensure well-posedness. Necessary optimality conditions for the optimal control problem are then derived. A convergent multi-parameter regularization is considered which addresses both, the possibly degenerate term in the equation and the state constraint. Some computational studies are then reported which evidence the relevant role of the state constraint, and motivate proper scalings of involved regularization and numerical parameters.

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