Parallel computing for rolling mill process with a numerical treatment of the LQR problem

The considerable increase in computation of the optimal control problems has in many cases overflowed the computing capacity available to handle complex systems in real time. For this reason, alternatives such as parallel computing are studied in this article, where the problem is worked out by dist...

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Authors: Gómez Múnera, John Anderson, Giraldo Quintero, Alejandro
Format: article
Status:Published version
Publication Date:2020
Country:Colombia
Institution:Corporación Universidad de la Costa
Repository:Repositorio REDICUC
Language:English
OAI Identifier:oai:repositorio.cuc.edu.co:11323/10334
Online Access:https://hdl.handle.net/11323/10334
https://repositorio.cuc.edu.co/
Access Level:Open access
Keyword:Automatic control
Chemical processes
Computer programming
Computer techniques
Multithreading
Parallel algorithms
Parallel processing
Control automático
Procesos químicos
Programación informática
Técnicas informáticas
Multihilo
Algoritmos paralelos
Procesamiento paralelo
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oai_identifier_str oai:repositorio.cuc.edu.co:11323/10334
network_acronym_str CO
network_name_str Colombia
repository_id_str
dc.title.none.fl_str_mv Parallel computing for rolling mill process with a numerical treatment of the LQR problem
Computación en paralelo para el proceso de laminación con un tratamiento numérico del problema LQR
title Parallel computing for rolling mill process with a numerical treatment of the LQR problem
spellingShingle Parallel computing for rolling mill process with a numerical treatment of the LQR problem
Gómez Múnera, John Anderson
Automatic control
Chemical processes
Computer programming
Computer techniques
Multithreading
Parallel algorithms
Parallel processing
Control automático
Procesos químicos
Programación informática
Técnicas informáticas
Multihilo
Algoritmos paralelos
Procesamiento paralelo
title_short Parallel computing for rolling mill process with a numerical treatment of the LQR problem
title_full Parallel computing for rolling mill process with a numerical treatment of the LQR problem
title_fullStr Parallel computing for rolling mill process with a numerical treatment of the LQR problem
title_full_unstemmed Parallel computing for rolling mill process with a numerical treatment of the LQR problem
title_sort Parallel computing for rolling mill process with a numerical treatment of the LQR problem
dc.creator.none.fl_str_mv Gómez Múnera, John Anderson
Giraldo Quintero, Alejandro
author Gómez Múnera, John Anderson
author_facet Gómez Múnera, John Anderson
Giraldo Quintero, Alejandro
author_role author
author2 Giraldo Quintero, Alejandro
author2_role author
dc.subject.none.fl_str_mv Automatic control
Chemical processes
Computer programming
Computer techniques
Multithreading
Parallel algorithms
Parallel processing
Control automático
Procesos químicos
Programación informática
Técnicas informáticas
Multihilo
Algoritmos paralelos
Procesamiento paralelo
topic Automatic control
Chemical processes
Computer programming
Computer techniques
Multithreading
Parallel algorithms
Parallel processing
Control automático
Procesos químicos
Programación informática
Técnicas informáticas
Multihilo
Algoritmos paralelos
Procesamiento paralelo
description The considerable increase in computation of the optimal control problems has in many cases overflowed the computing capacity available to handle complex systems in real time. For this reason, alternatives such as parallel computing are studied in this article, where the problem is worked out by distributing the tasks among several processors in order to accelerate the computation and to analyze and investigate the reduction of the total time of calculation the incremental gradually the processors used in it. We explore the use of these methods with a case study represented in a rolling mill process, and in turn making use of the strategy of updating the Phase Finals values for the construction of the final penalty matrix for the solution of the differential Riccati Equation. In addition, the order of the problem studied is increasing gradually for compare the improvements achieved in the models with major dimension. Parallel computing alternatives are also studied through multiple processing elements within a single machine or in a cluster via OpenMP, which is an Application Programming Interface (API) that allows the creation of shared memory programs.
publishDate 2020
dc.date.none.fl_str_mv 2020
2023-07-21T21:03:43Z
2023-07-21T21:03:43Z
dc.type.none.fl_str_mv Artículo de revista
http://purl.org/coar/resource_type/c_6501
Text
info:eu-repo/semantics/article
http://purl.org/redcol/resource_type/ART
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/version/c_970fb48d4fbd8a85
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv J. A. Gómez & A. Giraldo-Quintero, “Parallel Computing for Rolling Mill Process with a Numerical Treatment of the LQR Problem”, J. Comput. Electron. Sci.: Theory Appl., vol. 1, no. 1, pp. 11–30, 2020. https://doi.org/10.17981/cesta.01.01.2020.02
https://hdl.handle.net/11323/10334
10.17981/cesta.01.01.2020.02
2745-0090
Corporación Universidad de la Costa
REDICUC - Repositorio CUC
https://repositorio.cuc.edu.co/
identifier_str_mv J. A. Gómez & A. Giraldo-Quintero, “Parallel Computing for Rolling Mill Process with a Numerical Treatment of the LQR Problem”, J. Comput. Electron. Sci.: Theory Appl., vol. 1, no. 1, pp. 11–30, 2020. https://doi.org/10.17981/cesta.01.01.2020.02
10.17981/cesta.01.01.2020.02
2745-0090
Corporación Universidad de la Costa
REDICUC - Repositorio CUC
url https://hdl.handle.net/11323/10334
https://repositorio.cuc.edu.co/
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Computer and Electronic Sciences: Theory and Applications
[1] V. E. Sonzogni, A. M. Yommi, N. M. Nigro & M. A. Storti, “A parallel finite element program on a beowulf cluster,” Adv Eng Softw, vol. 33, no. 7, pp. 427–443, Jul. 2002. https://doi.org/10.1016/S0965-9978(02)00059-5
[2] J. D. Hennessy & D. A. Patterson, Arquitectura de computadores: Un enfoque cuantitativo. MD, Esp.: McGraw-Hill, 1993.
[3] M. Tokhi, M. A. Hossain & M. Shaheed, Parallel Computing for Real-Time Signal Processing and Control. London, UK: Springer, 2003.
[4] A. S. Tanenbaum, Sistemas operativos modernos. 3rd edición. MX, D.F., MX: Pearson Educación, 2009.
[5] P. Pardalos & R. Pytlak, Conjugate Gradient Algorithms In Nonconvex Optimization. NY, USA: Springer, 2008.
[6] A. A. Agrachev & Y. L. Sachkov, Control Theory from the Geometric Viewpoint. Bln-HDB: Springer-Verlag, 2004.
[7] M. Athans & P. Falb, Optimal Control: An Introduction to the Theory and Its Applications. NY, USA: Dover, 2006.
[8] V. Costanza & P. S. Rivadeneira, Enfoque Hamiltoniano al control optimo de sistemas dinámicos. SAANZ, DE: OmniScriptum, 2014.
[9] L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze & E. F. Mishchenko, The Mathematical Theory of Optimal Processes. NY, USA: Macmillan, 1964.
[10] J. L. Troutman, Variational Calculus and Optimal Control. NY, USA: Springer, 1996.
[11] V. Costanza & C. E. Neuman, “Partial differential equations for missing boundary conditions in the linear-quadratic optimal control problems,” Lat Am Appl Res, vol. 39, no. 3, pp. 207–212, Dec. 2009. Available: http://hdl.handle.net/11336/17096
[12] E. D. Sontag, Mathematical Control Theory. NY, USA: Springer, 1998.
[13] V. Costanza & C. E. Neuman, “Optimal control of nonlinear chemical reactors via an initial-value hamiltonian problem,” Optim Control Appl Methods, vol. 27, no. 1, pp. 41–60, Jan. 2006. http://dx.doi.org/10.1002/oca.772
[14] A. Kojima & M. Morari, “LQ control for constrained continuous-time systems,” Automatica, vol. 40, no. 7, pp. 1143–1155, Jul. 2004. https://doi.org/10.1016/j.automatica.2004.02.007
[15] S. J. Qin & T. A. Badgwell, “A survey of industrial model predictive control technology,” Control Eng Pract, vol. 11, no. 7, pp. 733–764, Jul. 2003. https://doi.org/10.1016/S0967-0661(02)00186-7
[16] O. J. Rojas, G. C. Goodwin, M. M. Seron & A. Feuer, “An svd based´ strategy for receding horizon control of input constrained linear systems,” Int J Robust Nonlin, vol. 14, no. 13-14, pp. 1207–1226, May. 2004. https://doi.org/10.1002/rnc.940
[17] J. L. Speyer & D. H. Jacobson, Primer on Optimal Control Theory. Phila, USA: SIAM Books, 2010.
[18] V. Costanza & P. S. Rivadeneira, “Optimal satured feedback laws for LQR problems with bounded controls,” Comput Appl Math, vol. 32, no. 2, pp. 355–371, Mar. 2013. https://doi.org/10.1007/s40314-013-0025-7
[19] V. Costanza, P. S. Rivadeneira & J. A. Gómez, “An efficient cost reduction procedure for bounded-control LQR problems,” Comput Appl Math, vol. 37, no. 2, pp. 1175–1196, Oct. 2016. https://doi.org/10.1007/s40314-016-0393-x
[20] V. Costanza, P. S. Rivadeneira & J. A. Gómez, “Numerical treatment of the bounded-control lqr problem by updating the final phase value,” IEEE Lat Ame T, vol. 14, no. 6, pp. 2687–2692, Jun. 2016. https://doi.org/10.1109/TLA.2016.7555239
[21] V. Costanza & P. S. Rivadeneira, “Online suboptimal control of linearized models,” Syst Sci Control Eng, vol. 2, no. 1, pp. 379–388, Dec. 2014. https://doi.org/10.1080/21642583.2014.913215
[22] E. Bramanti, M. Bramanti, P. Stiavetti & E. Benedetti, “A frequency deconvolution procedure using a conjugate gradient minimization method with suitable constraints,” J Chemom, vol. 8, no. 6, pp. 409–421, Dec. 1994. https://doi.org/10.1002/ cem.1180080606
[23] R. Fletcher & C. M. Reeves, “Function minimization for conjugate gradients,” Computer J, vol. 7, no. 2, pp. 149–154, Jan. 1964. https://doi.org/10.1093/comjnl/7.2.149
[24] A. V. Rao, D. A. Benson, G. T. Huntington, C. Francolin, C. L. Darby & M. A. Patterson, “User’s manual for GPOPS: A matlab package for dynamic optimization using the gauss pseudospectral method,” UF, GVL; USA, Tech. Rep., Aug. 2008.
[25] P. Bernhard, “Introduccion a la teoría de control Optimo,” Inst. Mat. Beppo Levi, ROS, AR, Tech. Rep., Cuaderno No. 4, 1972.
[26] V. Costanza, P. S. Rivadeneira & R. D. Spies, “Equations for the missing boundary values in the hamiltonian formulation of optimal control problems,” J Optim Theory and Appl, vol. 149, no. 1, pp. 26–46, Jan. 2011. https://doi.org/10.1007/s10957-010- 9773-3
[27] G. C. Goodwin, S. F. Graebe & M. E. Salgado, Control system design, vol. 240. NJ, USA: Prentice Hall, 2001.
30
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1
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rights_invalid_str_mv © The author; licensee Universidad de la Costa - CUC.
Atribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)
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dc.publisher.none.fl_str_mv Corporación Universidad de la Costa
Colombia
publisher.none.fl_str_mv Corporación Universidad de la Costa
Colombia
dc.source.none.fl_str_mv https://revistascientificas.cuc.edu.co/CESTA/article/view/3376
reponame:Repositorio REDICUC
instname:Corporación Universidad de la Costa
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spelling Parallel computing for rolling mill process with a numerical treatment of the LQR problemComputación en paralelo para el proceso de laminación con un tratamiento numérico del problema LQRGómez Múnera, John AndersonGiraldo Quintero, AlejandroAutomatic controlChemical processesComputer programmingComputer techniquesMultithreadingParallel algorithmsParallel processingControl automáticoProcesos químicosProgramación informáticaTécnicas informáticasMultihiloAlgoritmos paralelosProcesamiento paraleloThe considerable increase in computation of the optimal control problems has in many cases overflowed the computing capacity available to handle complex systems in real time. For this reason, alternatives such as parallel computing are studied in this article, where the problem is worked out by distributing the tasks among several processors in order to accelerate the computation and to analyze and investigate the reduction of the total time of calculation the incremental gradually the processors used in it. We explore the use of these methods with a case study represented in a rolling mill process, and in turn making use of the strategy of updating the Phase Finals values for the construction of the final penalty matrix for the solution of the differential Riccati Equation. In addition, the order of the problem studied is increasing gradually for compare the improvements achieved in the models with major dimension. Parallel computing alternatives are also studied through multiple processing elements within a single machine or in a cluster via OpenMP, which is an Application Programming Interface (API) that allows the creation of shared memory programs.El considerable aumento en el cómputo de los problemas de control óptimo ha desbordado en muchos casos la capacidad de computación disponible para manejar sistemas complejos en tiempo real. Por esta razón, en este artículo se estudian alternativas como la computación paralela, donde el problema se resuelve distribuyendo las tareas entre varios procesadores para acelerar el cómputo y para analizar e investigar la reducción del tiempo total de cálculo incrementando gradualmente los procesadores utilizados en él. Exploramos el uso de estos métodos con un estudio de caso representado en un proceso de laminación, y a su vez haciendo uso de la estrategia de actualización de los valores de las fases finales para la construcción de la matriz de penalización final para la solución de la ecuación de Riccati diferencial. Además, el orden del problema estudiado va aumentando gradualmente para comparar las mejoras logradas en los modelos de mayor dimensión. También se estudian alternativas de computación paralela a través de múltiples elementos de procesamiento dentro de una sola máquina o en un clúster mediante OpenMP, que es una Interfaz de Programación de Aplicaciones (API) que permite la creación de programas de memoria compartida.Corporación Universidad de la CostaColombia2023-07-21T21:03:43Z2023-07-21T21:03:43Z2020Artículo de revistahttp://purl.org/coar/resource_type/c_6501Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a8520 páginasapplication/pdfapplication/pdfJ. A. Gómez & A. Giraldo-Quintero, “Parallel Computing for Rolling Mill Process with a Numerical Treatment of the LQR Problem”, J. Comput. Electron. Sci.: Theory Appl., vol. 1, no. 1, pp. 11–30, 2020. https://doi.org/10.17981/cesta.01.01.2020.02https://hdl.handle.net/11323/1033410.17981/cesta.01.01.2020.022745-0090Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/https://revistascientificas.cuc.edu.co/CESTA/article/view/3376reponame:Repositorio REDICUCinstname:Corporación Universidad de la Costainstacron:Corporación Universidad de la CostaengComputer and Electronic Sciences: Theory and Applications[1] V. E. Sonzogni, A. M. Yommi, N. M. Nigro & M. A. Storti, “A parallel finite element program on a beowulf cluster,” Adv Eng Softw, vol. 33, no. 7, pp. 427–443, Jul. 2002. https://doi.org/10.1016/S0965-9978(02)00059-5[2] J. D. Hennessy & D. A. Patterson, Arquitectura de computadores: Un enfoque cuantitativo. MD, Esp.: McGraw-Hill, 1993.[3] M. Tokhi, M. A. Hossain & M. Shaheed, Parallel Computing for Real-Time Signal Processing and Control. London, UK: Springer, 2003.[4] A. S. Tanenbaum, Sistemas operativos modernos. 3rd edición. MX, D.F., MX: Pearson Educación, 2009.[5] P. Pardalos & R. Pytlak, Conjugate Gradient Algorithms In Nonconvex Optimization. NY, USA: Springer, 2008.[6] A. A. Agrachev & Y. L. Sachkov, Control Theory from the Geometric Viewpoint. Bln-HDB: Springer-Verlag, 2004.[7] M. Athans & P. Falb, Optimal Control: An Introduction to the Theory and Its Applications. NY, USA: Dover, 2006.[8] V. Costanza & P. S. Rivadeneira, Enfoque Hamiltoniano al control optimo de sistemas dinámicos. SAANZ, DE: OmniScriptum, 2014.[9] L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze & E. F. Mishchenko, The Mathematical Theory of Optimal Processes. NY, USA: Macmillan, 1964.[10] J. L. Troutman, Variational Calculus and Optimal Control. NY, USA: Springer, 1996.[11] V. Costanza & C. E. Neuman, “Partial differential equations for missing boundary conditions in the linear-quadratic optimal control problems,” Lat Am Appl Res, vol. 39, no. 3, pp. 207–212, Dec. 2009. Available: http://hdl.handle.net/11336/17096[12] E. D. Sontag, Mathematical Control Theory. NY, USA: Springer, 1998.[13] V. Costanza & C. E. Neuman, “Optimal control of nonlinear chemical reactors via an initial-value hamiltonian problem,” Optim Control Appl Methods, vol. 27, no. 1, pp. 41–60, Jan. 2006. http://dx.doi.org/10.1002/oca.772[14] A. Kojima & M. Morari, “LQ control for constrained continuous-time systems,” Automatica, vol. 40, no. 7, pp. 1143–1155, Jul. 2004. https://doi.org/10.1016/j.automatica.2004.02.007[15] S. J. Qin & T. A. Badgwell, “A survey of industrial model predictive control technology,” Control Eng Pract, vol. 11, no. 7, pp. 733–764, Jul. 2003. https://doi.org/10.1016/S0967-0661(02)00186-7[16] O. J. Rojas, G. C. Goodwin, M. M. Seron & A. Feuer, “An svd based´ strategy for receding horizon control of input constrained linear systems,” Int J Robust Nonlin, vol. 14, no. 13-14, pp. 1207–1226, May. 2004. https://doi.org/10.1002/rnc.940[17] J. L. Speyer & D. H. Jacobson, Primer on Optimal Control Theory. Phila, USA: SIAM Books, 2010.[18] V. Costanza & P. S. Rivadeneira, “Optimal satured feedback laws for LQR problems with bounded controls,” Comput Appl Math, vol. 32, no. 2, pp. 355–371, Mar. 2013. https://doi.org/10.1007/s40314-013-0025-7[19] V. Costanza, P. S. Rivadeneira & J. A. Gómez, “An efficient cost reduction procedure for bounded-control LQR problems,” Comput Appl Math, vol. 37, no. 2, pp. 1175–1196, Oct. 2016. https://doi.org/10.1007/s40314-016-0393-x[20] V. Costanza, P. S. Rivadeneira & J. A. Gómez, “Numerical treatment of the bounded-control lqr problem by updating the final phase value,” IEEE Lat Ame T, vol. 14, no. 6, pp. 2687–2692, Jun. 2016. https://doi.org/10.1109/TLA.2016.7555239[21] V. Costanza & P. S. Rivadeneira, “Online suboptimal control of linearized models,” Syst Sci Control Eng, vol. 2, no. 1, pp. 379–388, Dec. 2014. https://doi.org/10.1080/21642583.2014.913215[22] E. Bramanti, M. Bramanti, P. Stiavetti & E. Benedetti, “A frequency deconvolution procedure using a conjugate gradient minimization method with suitable constraints,” J Chemom, vol. 8, no. 6, pp. 409–421, Dec. 1994. https://doi.org/10.1002/ cem.1180080606[23] R. Fletcher & C. M. Reeves, “Function minimization for conjugate gradients,” Computer J, vol. 7, no. 2, pp. 149–154, Jan. 1964. https://doi.org/10.1093/comjnl/7.2.149[24] A. V. Rao, D. A. Benson, G. T. Huntington, C. Francolin, C. L. Darby & M. A. Patterson, “User’s manual for GPOPS: A matlab package for dynamic optimization using the gauss pseudospectral method,” UF, GVL; USA, Tech. Rep., Aug. 2008.[25] P. Bernhard, “Introduccion a la teoría de control Optimo,” Inst. Mat. Beppo Levi, ROS, AR, Tech. Rep., Cuaderno No. 4, 1972.[26] V. Costanza, P. S. Rivadeneira & R. D. Spies, “Equations for the missing boundary values in the hamiltonian formulation of optimal control problems,” J Optim Theory and Appl, vol. 149, no. 1, pp. 26–46, Jan. 2011. https://doi.org/10.1007/s10957-010- 9773-3[27] G. C. Goodwin, S. F. Graebe & M. E. Salgado, Control system design, vol. 240. NJ, USA: Prentice Hall, 2001.301111© The author; licensee Universidad de la Costa - CUC.Atribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf22024-09-17T19:22:24Z
score 15,812429

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