Optimal Control of Temperature in Fluid Flow Using Four Types of MinimizationTechniques
The purpose of this paper is a thermal optimal control problem using four types of minimization technique. The four types of minimization techniques are the weighted gradient method, the Newton based method, the modified steepest descent method and the steepest descent method using weighting adaptat...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SAGE Publishing
2010-06-01
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| Series: | Journal of Algorithms & Computational Technology |
| Online Access: | https://doi.org/10.1260/1748-3018.4.2.207 |
| _version_ | 1811286753800093696 |
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| author | Daisuke Yamazaki Mutsuto Kawahara |
| author_facet | Daisuke Yamazaki Mutsuto Kawahara |
| author_sort | Daisuke Yamazaki |
| collection | DOAJ |
| description | The purpose of this paper is a thermal optimal control problem using four types of minimization technique. The four types of minimization techniques are the weighted gradient method, the Newton based method, the modified steepest descent method and the steepest descent method using weighting adaptation. The formulation is based on the optimal control theory in which the performance function is expressed by the computed and targeted temperatures. The optimal values can be obtained by minimizing the performance function. The thermal fluid flow is described by the Boussinesq approximated incompressible Navier-Stokes equation and the energy equation is analyzed. BFGS is applied to calculate the Hessian matrix which is used in the Newton-based method. The traction given by the perturbation for the Lagrange multiplier is used in the BFGS method. |
| first_indexed | 2024-04-13T03:05:41Z |
| format | Article |
| id | doaj.art-838ab9fdf3f34227acf2ea54f4a00d3e |
| institution | Directory Open Access Journal |
| issn | 1748-3018 1748-3026 |
| language | English |
| last_indexed | 2024-04-13T03:05:41Z |
| publishDate | 2010-06-01 |
| publisher | SAGE Publishing |
| record_format | Article |
| series | Journal of Algorithms & Computational Technology |
| spelling | doaj.art-838ab9fdf3f34227acf2ea54f4a00d3e2022-12-22T03:05:15ZengSAGE PublishingJournal of Algorithms & Computational Technology1748-30181748-30262010-06-01410.1260/1748-3018.4.2.207Optimal Control of Temperature in Fluid Flow Using Four Types of MinimizationTechniquesDaisuke YamazakiMutsuto KawaharaThe purpose of this paper is a thermal optimal control problem using four types of minimization technique. The four types of minimization techniques are the weighted gradient method, the Newton based method, the modified steepest descent method and the steepest descent method using weighting adaptation. The formulation is based on the optimal control theory in which the performance function is expressed by the computed and targeted temperatures. The optimal values can be obtained by minimizing the performance function. The thermal fluid flow is described by the Boussinesq approximated incompressible Navier-Stokes equation and the energy equation is analyzed. BFGS is applied to calculate the Hessian matrix which is used in the Newton-based method. The traction given by the perturbation for the Lagrange multiplier is used in the BFGS method.https://doi.org/10.1260/1748-3018.4.2.207 |
| spellingShingle | Daisuke Yamazaki Mutsuto Kawahara Optimal Control of Temperature in Fluid Flow Using Four Types of MinimizationTechniques Journal of Algorithms & Computational Technology |
| title | Optimal Control of Temperature in Fluid Flow Using Four Types of MinimizationTechniques |
| title_full | Optimal Control of Temperature in Fluid Flow Using Four Types of MinimizationTechniques |
| title_fullStr | Optimal Control of Temperature in Fluid Flow Using Four Types of MinimizationTechniques |
| title_full_unstemmed | Optimal Control of Temperature in Fluid Flow Using Four Types of MinimizationTechniques |
| title_short | Optimal Control of Temperature in Fluid Flow Using Four Types of MinimizationTechniques |
| title_sort | optimal control of temperature in fluid flow using four types of minimizationtechniques |
| url | https://doi.org/10.1260/1748-3018.4.2.207 |
| work_keys_str_mv | AT daisukeyamazaki optimalcontroloftemperatureinfluidflowusingfourtypesofminimizationtechniques AT mutsutokawahara optimalcontroloftemperatureinfluidflowusingfourtypesofminimizationtechniques |