Optimization-Based Control of Constrained Nonlinear Systems with Continuous-Time Models: Adaptive Time-Grid Refinement Algorithms
Autor(a) principal: | |
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Data de Publicação: | 2016 |
Outros Autores: | |
Tipo de documento: | Livro |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | https://repositorio-aberto.up.pt/handle/10216/116881 |
Resumo: | We address optimal control problems for nonlinear systems with pathwise state-constraints. These are challenging nonlinear problems for which the number of discretization points is a major factor determining the computational time. Also, the location of these points has a major impact in the accuracy of the solutions. We propose an algorithm that iteratively finds an adequate time-grid to satisfy some predefined error estimate on the obtained trajectories, which is guided by information on the adjoint multipliers. The obtained results show a highly favorable comparison against the traditional equidistant spaced time grid methods, including the ones using discrete time models. This way, continuous time plant models can be directly used. The discretization procedure can be automated and there is no need to select a priori the adequate time step. Even if the optimization procedure is forced to stop in an early stage, as might be the case in real time problems, we can still obtain a meaningful solution, although it might be a less accurate one. The extension of the procedure to a Model Predictive Control (MPC) context is proposed here. By defining a time dependent accuracy threshold, we can generate solutions that are more accurate in the initial parts of the receding horizon, which are the most relevant for MPC. |
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spelling |
Optimization-Based Control of Constrained Nonlinear Systems with Continuous-Time Models: Adaptive Time-Grid Refinement AlgorithmsWe address optimal control problems for nonlinear systems with pathwise state-constraints. These are challenging nonlinear problems for which the number of discretization points is a major factor determining the computational time. Also, the location of these points has a major impact in the accuracy of the solutions. We propose an algorithm that iteratively finds an adequate time-grid to satisfy some predefined error estimate on the obtained trajectories, which is guided by information on the adjoint multipliers. The obtained results show a highly favorable comparison against the traditional equidistant spaced time grid methods, including the ones using discrete time models. This way, continuous time plant models can be directly used. The discretization procedure can be automated and there is no need to select a priori the adequate time step. Even if the optimization procedure is forced to stop in an early stage, as might be the case in real time problems, we can still obtain a meaningful solution, although it might be a less accurate one. The extension of the procedure to a Model Predictive Control (MPC) context is proposed here. By defining a time dependent accuracy threshold, we can generate solutions that are more accurate in the initial parts of the receding horizon, which are the most relevant for MPC.2016-102016-10-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/bookapplication/pdfhttps://repositorio-aberto.up.pt/handle/10216/116881eng10.1063/1.4965373fontes, faccL.T. Paivainfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-29T13:02:09Zoai:repositorio-aberto.up.pt:10216/116881Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T23:32:15.224943Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Optimization-Based Control of Constrained Nonlinear Systems with Continuous-Time Models: Adaptive Time-Grid Refinement Algorithms |
title |
Optimization-Based Control of Constrained Nonlinear Systems with Continuous-Time Models: Adaptive Time-Grid Refinement Algorithms |
spellingShingle |
Optimization-Based Control of Constrained Nonlinear Systems with Continuous-Time Models: Adaptive Time-Grid Refinement Algorithms fontes, facc |
title_short |
Optimization-Based Control of Constrained Nonlinear Systems with Continuous-Time Models: Adaptive Time-Grid Refinement Algorithms |
title_full |
Optimization-Based Control of Constrained Nonlinear Systems with Continuous-Time Models: Adaptive Time-Grid Refinement Algorithms |
title_fullStr |
Optimization-Based Control of Constrained Nonlinear Systems with Continuous-Time Models: Adaptive Time-Grid Refinement Algorithms |
title_full_unstemmed |
Optimization-Based Control of Constrained Nonlinear Systems with Continuous-Time Models: Adaptive Time-Grid Refinement Algorithms |
title_sort |
Optimization-Based Control of Constrained Nonlinear Systems with Continuous-Time Models: Adaptive Time-Grid Refinement Algorithms |
author |
fontes, facc |
author_facet |
fontes, facc L.T. Paiva |
author_role |
author |
author2 |
L.T. Paiva |
author2_role |
author |
dc.contributor.author.fl_str_mv |
fontes, facc L.T. Paiva |
description |
We address optimal control problems for nonlinear systems with pathwise state-constraints. These are challenging nonlinear problems for which the number of discretization points is a major factor determining the computational time. Also, the location of these points has a major impact in the accuracy of the solutions. We propose an algorithm that iteratively finds an adequate time-grid to satisfy some predefined error estimate on the obtained trajectories, which is guided by information on the adjoint multipliers. The obtained results show a highly favorable comparison against the traditional equidistant spaced time grid methods, including the ones using discrete time models. This way, continuous time plant models can be directly used. The discretization procedure can be automated and there is no need to select a priori the adequate time step. Even if the optimization procedure is forced to stop in an early stage, as might be the case in real time problems, we can still obtain a meaningful solution, although it might be a less accurate one. The extension of the procedure to a Model Predictive Control (MPC) context is proposed here. By defining a time dependent accuracy threshold, we can generate solutions that are more accurate in the initial parts of the receding horizon, which are the most relevant for MPC. |
publishDate |
2016 |
dc.date.none.fl_str_mv |
2016-10 2016-10-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/book |
format |
book |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://repositorio-aberto.up.pt/handle/10216/116881 |
url |
https://repositorio-aberto.up.pt/handle/10216/116881 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1063/1.4965373 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
|
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1799135632980705280 |