Optimal actuator location for time and norm optimal control of null controllable heat equation

2014 ◽  
Vol 27 (1) ◽  
pp. 23-48 ◽  
Author(s):  
Bao-Zhu Guo ◽  
Dong-Hui Yang
Keyword(s):  
Optimal Control ◽  
Heat Equation

Stability of optimal control of heat equation with singular potential

2014 ◽  
Vol 74 ◽  
pp. 18-23 ◽  
Author(s):  
Guojie Zheng ◽  
Bao-Zhu Guo ◽  
M. Montaz Ali
Keyword(s):  
Optimal Control ◽  
Heat Equation ◽  
Singular Potential

Optimal control of the heat equation in an inhomogeneous body

2004 ◽  
Vol 15 (1-2) ◽  
pp. 127-146 ◽  
Author(s):  
A. H. Borzabadi ◽  
A. V. Kamyad ◽  
M. H. Farahi
Keyword(s):  
Optimal Control ◽  
Heat Equation ◽  
Inhomogeneous Body

scholarly journals Sparse optimal control for a semilinear heat equation with mixed control-state constraints - regularity of Lagrange multipliers

2020 ◽  
Author(s):  
Fredi Tröltzsch ◽  
Eduardo Casas
Keyword(s):  
Optimal Control ◽  
Heat Equation ◽  
Lagrange Multipliers ◽  
State Constraints ◽  
Optimal Solution ◽  
Structural Condition ◽  
Semilinear Heat Equation ◽  
Mixed Control ◽  
Quadratic Tracking ◽  
Control State

An optimal control problem for a semilinear heat equation with distributed control is discussed, where two-sided pointwise box constraints on the control and two-sided pointwise mixed control-state constraints are given.   The objective functional is the sum of a standard quadratic tracking type part and a multiple of the $L^1$-norm of the control that accounts for sparsity. Under a certain structural condition on almost active sets of the optimal solution, the existence of integrable Lagrange multipliers is proved for all inequality constraints. For this purpose, a theorem by Yosida and Hewitt is used. It is shown that the structural condition is fulfilled for all sufficiently large sparsity parameters. The sparsity of the optimal control is investigated. Eventually, higher smoothness of Lagrange multipliers is shown up to H\"older regularity.

scholarly journals Optimal control for a phase field model of melting arising from inductive heating

2022 ◽  
Vol 7 (1) ◽  
pp. 121-142
Author(s):  
Zonghong Xiong ◽  
◽  
Wei Wei ◽  
Ying Zhou ◽  
Yue Wang ◽  
...  
Keyword(s):  
Optimal Control ◽  
Field Equation ◽  
Heat Equation ◽  
Induction Heating ◽  
Phase Field ◽  
Control Variable ◽  
Melting Process ◽  
Inductive Heating ◽  
Controlled System ◽  
Metal Melting

<abstract><p>Due to its unique performance of high efficiency, fast heating speed and low power consumption, induction heating is widely and commonly used in many applications. In this paper, we study an optimal control problem arising from a metal melting process by using a induction heating method. Metal melting phenomena can be modeled by phase field equations. The aim of optimization is to approximate a desired temperature evolution and melting process. The controlled system is obtained by coupling Maxwell's equations, heat equation and phase field equation. The control variable of the system is the external electric field on the local boundary. The existence and uniqueness of the solution of the controlled system are showed by using Galerkin's method and Leray-Schauder's fixed point theorem. By proving that the control-to-state operator $ P $ is weakly sequentially continuous and Fréchet differentiable, we establish an existence result of optimal control and derive the first-order necessary optimality conditions. This work improves the limitation of the previous control system which only contains heat equation and phase field equation.</p></abstract>

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