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...

Full description

Autores:
Gómez Múnera, John Anderson
Giraldo Quintero, Alejandro
Tipo de recurso:
Article of journal
Fecha de publicación:
2021
Institución:
Corporación Universidad de la Costa
Repositorio:
REDICUC - Repositorio CUC
Idioma:
eng
OAI Identifier:
oai:repositorio.cuc.edu.co:11323/8869
Acceso en línea:
https://hdl.handle.net/11323/8869
https://doi.org/10.17981/cesta.01.01.2020.02
https://repositorio.cuc.edu.co/
Palabra clave:
Automatic control
Chemical processes
Computer programming
Computer techniques
Multithreading
Parallel algorithms
Parallel processing
Control automático
Rights
openAccess
License
Atribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)
id RCUC2_b2db5a3de700e02293fc565bbdb0c00c
oai_identifier_str oai:repositorio.cuc.edu.co:11323/8869
network_acronym_str RCUC2
network_name_str REDICUC - Repositorio CUC
repository_id_str
dc.title.spa.fl_str_mv Parallel Computing for Rolling Mill Process with a Numerical Treatment of the LQR Problem
dc.title.translated.spa.fl_str_mv Computación en paralelo para el proceso de laminación con un tratamiento numérico del problema de 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
Automatic control
Chemical processes
Computer programming
Computer techniques
Multithreading
Parallel algorithms
Parallel processing
Control automático
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.fl_str_mv Gómez Múnera, John Anderson
Giraldo Quintero, Alejandro
dc.contributor.author.spa.fl_str_mv Gómez Múnera, John Anderson
Giraldo Quintero, Alejandro
dc.subject.proposal.eng.fl_str_mv Automatic control
Chemical processes
Computer programming
Computer techniques
Multithreading
Parallel algorithms
Parallel processing
topic Automatic control
Chemical processes
Computer programming
Computer techniques
Multithreading
Parallel algorithms
Parallel processing
Control automático
dc.subject.proposal.spa.fl_str_mv Control automático
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 2021
dc.date.accessioned.none.fl_str_mv 2021-11-17T02:40:50Z
dc.date.available.none.fl_str_mv 2021-11-17T02:40:50Z
dc.date.issued.none.fl_str_mv 2021
dc.type.spa.fl_str_mv Artículo de revista
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.coar.spa.fl_str_mv http://purl.org/coar/resource_type/c_6501
dc.type.content.spa.fl_str_mv Text
dc.type.driver.spa.fl_str_mv info:eu-repo/semantics/article
dc.type.redcol.spa.fl_str_mv http://purl.org/redcol/resource_type/ART
dc.type.version.spa.fl_str_mv info:eu-repo/semantics/acceptedVersion
format http://purl.org/coar/resource_type/c_6501
status_str acceptedVersion
dc.identifier.citation.spa.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
dc.identifier.uri.spa.fl_str_mv https://hdl.handle.net/11323/8869
dc.identifier.url.spa.fl_str_mv https://doi.org/10.17981/cesta.01.01.2020.02
dc.identifier.doi.spa.fl_str_mv 10.17981/cesta.01.01.2020.02
dc.identifier.eissn.spa.fl_str_mv 2745-0090
dc.identifier.instname.spa.fl_str_mv Corporación Universidad de la Costa
dc.identifier.reponame.spa.fl_str_mv REDICUC - Repositorio CUC
dc.identifier.repourl.spa.fl_str_mv 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/11323/8869
https://doi.org/10.17981/cesta.01.01.2020.02
https://repositorio.cuc.edu.co/
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.ispartofjournal.spa.fl_str_mv Computer and Electronic Sciences: Theory and Applications
Computer and Electronic Sciences: Theory and Applications
dc.relation.references.spa.fl_str_mv [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.
[28] W. S. Levine, The control handbook. BOCCA, USA: CRC Press, 1996.
[29] J.-J. E. Slotine & W. Li, Applied nonlinear control, vol. 199, no. 1. NJ, ENGI: Prentice-Hall, 1991.
[30] V. Costanza & P. S. Rivadeneira, “Partially-Regular Bounded-Control Problems for Nonlinear Systems,” in Conf. Proc. XXIV Congreso Argentino de Control Automático, AADECA, BA, AR, 27-29 Oct. 2014.
[31] J. A. Gómez, P. S. Rivadeneira & V. Costanza, “A cost reduction procedure for control-restricted nonlinear systems,” IREACO, vol. 10, no. 6, pp. 1–24, Nov. 2017. https://doi.org/10.15866/ireaco.v10i6.13820
[32] B. Chapman, G. Jost & R. Van Der Pas, Using OpenMP. CAM, MA, USA: MIT Press, 2008.
[33] V. Dhamo & F. Troltzsch, “Some aspects of reachability for parabolic¨ boundary control problems with control constraints,” Comput Optim Appl, vol. 50, no. 1, pp. 75–110, Oct. 2008. https://doi.org/10.1007/s10589-009-9310-1
[34] G. Hearns & M. J. Grimble, “Temperature control in transport delay systems,” in Proc. 2010 American Control Conference, IEEE, Baltimore, MD, USA, 30 Jun-2 Jul. 2010, pp. 6089–6094. https://doi.org/10.1109/ACC.2010.5531540
[35] C. Sanderson & R. Curtin, “Armadillo: a template-based c++ library for linear algebra,” J Open Source Softw, vol. 1, no. 2, pp. 1–2, Jun. 2016. https://doi.org/10.21105/joss.00026
dc.relation.citationendpage.none.fl_str_mv 30
dc.relation.citationstartpage.none.fl_str_mv 11
dc.relation.citationissue.spa.fl_str_mv 1
dc.relation.citationvolume.spa.fl_str_mv 1
dc.relation.ispartofjournalabbrev.spa.fl_str_mv CESTA
dc.rights.spa.fl_str_mv Atribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)
© The author; licensee Universidad de la Costa - CUC.
dc.rights.uri.spa.fl_str_mv http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.accessrights.spa.fl_str_mv info:eu-repo/semantics/openAccess
dc.rights.coar.spa.fl_str_mv http://purl.org/coar/access_right/c_abf2
rights_invalid_str_mv Atribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)
© The author; licensee Universidad de la Costa - CUC.
http://creativecommons.org/licenses/by-nc-nd/4.0/
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.extent.spa.fl_str_mv 20 páginas
dc.format.mimetype.spa.fl_str_mv application/pdf
dc.publisher.spa.fl_str_mv Corporación Universidad de la Costa
dc.publisher.place.spa.fl_str_mv Barranquilla
dc.source.spa.fl_str_mv Computer and Electronic Sciences: Theory and Applications
institution Corporación Universidad de la Costa
dc.source.url.spa.fl_str_mv https://revistascientificas.cuc.edu.co/CESTA/article/view/3376
bitstream.url.fl_str_mv https://repositorio.cuc.edu.co/bitstream/11323/8869/1/Vol1-02.pdf
https://repositorio.cuc.edu.co/bitstream/11323/8869/2/license_rdf
https://repositorio.cuc.edu.co/bitstream/11323/8869/3/license.txt
https://repositorio.cuc.edu.co/bitstream/11323/8869/4/Vol1-02.pdf.jpg
https://repositorio.cuc.edu.co/bitstream/11323/8869/5/Vol1-02.pdf.txt
bitstream.checksum.fl_str_mv c6a9e2f326d62dcc813dba3896c2317e
4460e5956bc1d1639be9ae6146a50347
e30e9215131d99561d40d6b0abbe9bad
29320a096dbc1672691ddfd26f2a1207
d7db874313c176b6d342658a0209c47b
bitstream.checksumAlgorithm.fl_str_mv MD5
MD5
MD5
MD5
MD5
repository.name.fl_str_mv Repositorio Universidad de La Costa
repository.mail.fl_str_mv bdigital@metabiblioteca.com
_version_ 1808400189386391552
spelling Gómez Múnera, John Andersonb6c55e989283e0528bbf09d26c9892f9Giraldo Quintero, Alejandro9d78727ed2749a3c5a0707eee1f455ef2021-11-17T02:40:50Z2021-11-17T02:40:50Z2021J. 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/11323/8869https://doi.org/10.17981/cesta.01.01.2020.0210.17981/cesta.01.01.2020.022745-0090Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/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.20 páginasapplication/pdfengCorporación Universidad de la CostaBarranquillaAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)© The author; licensee Universidad de la Costa - CUC.http://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Computer and Electronic Sciences: Theory and Applicationshttps://revistascientificas.cuc.edu.co/CESTA/article/view/3376Parallel 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 de LQRArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/acceptedVersionComputer and Electronic Sciences: Theory and ApplicationsComputer 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.[28] W. S. Levine, The control handbook. BOCCA, USA: CRC Press, 1996.[29] J.-J. E. Slotine & W. Li, Applied nonlinear control, vol. 199, no. 1. NJ, ENGI: Prentice-Hall, 1991.[30] V. Costanza & P. S. Rivadeneira, “Partially-Regular Bounded-Control Problems for Nonlinear Systems,” in Conf. Proc. XXIV Congreso Argentino de Control Automático, AADECA, BA, AR, 27-29 Oct. 2014.[31] J. A. Gómez, P. S. Rivadeneira & V. Costanza, “A cost reduction procedure for control-restricted nonlinear systems,” IREACO, vol. 10, no. 6, pp. 1–24, Nov. 2017. https://doi.org/10.15866/ireaco.v10i6.13820[32] B. Chapman, G. Jost & R. Van Der Pas, Using OpenMP. CAM, MA, USA: MIT Press, 2008.[33] V. Dhamo & F. Troltzsch, “Some aspects of reachability for parabolic¨ boundary control problems with control constraints,” Comput Optim Appl, vol. 50, no. 1, pp. 75–110, Oct. 2008. https://doi.org/10.1007/s10589-009-9310-1[34] G. Hearns & M. J. Grimble, “Temperature control in transport delay systems,” in Proc. 2010 American Control Conference, IEEE, Baltimore, MD, USA, 30 Jun-2 Jul. 2010, pp. 6089–6094. https://doi.org/10.1109/ACC.2010.5531540[35] C. Sanderson & R. Curtin, “Armadillo: a template-based c++ library for linear algebra,” J Open Source Softw, vol. 1, no. 2, pp. 1–2, Jun. 2016. https://doi.org/10.21105/joss.00026301111CESTAAutomatic controlChemical processesComputer programmingComputer techniquesMultithreadingParallel algorithmsParallel processingControl automáticoORIGINALVol1-02.pdfVol1-02.pdfapplication/pdf1506057https://repositorio.cuc.edu.co/bitstream/11323/8869/1/Vol1-02.pdfc6a9e2f326d62dcc813dba3896c2317eMD51open accessCC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8805https://repositorio.cuc.edu.co/bitstream/11323/8869/2/license_rdf4460e5956bc1d1639be9ae6146a50347MD52open accessLICENSElicense.txtlicense.txttext/plain; charset=utf-83196https://repositorio.cuc.edu.co/bitstream/11323/8869/3/license.txte30e9215131d99561d40d6b0abbe9badMD53open accessTHUMBNAILVol1-02.pdf.jpgVol1-02.pdf.jpgimage/jpeg71252https://repositorio.cuc.edu.co/bitstream/11323/8869/4/Vol1-02.pdf.jpg29320a096dbc1672691ddfd26f2a1207MD54open accessTEXTVol1-02.pdf.txtVol1-02.pdf.txttext/plain43763https://repositorio.cuc.edu.co/bitstream/11323/8869/5/Vol1-02.pdf.txtd7db874313c176b6d342658a0209c47bMD55open access11323/8869oai:repositorio.cuc.edu.co:11323/88692023-12-14 16:29:10.704Attribution-NonCommercial-NoDerivatives 4.0 International|||http://creativecommons.org/licenses/by-nc-nd/4.0/open accessRepositorio Universidad de La Costabdigital@metabiblioteca.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

Publicaciones similares