Testing of linear models for optimal control of second-order dynamical system based on model-reality differences

In this paper, the testing of linear models with different parameter values is conducted for solving the optimal control problem of a second-order dynamical system. The purpose of this testing is to provide the solution with the same structure but different parameter values in the model used. For do...

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Main Authors: Kek, Sie Long, Sim, Sy Yi, Chen, Chuei Yee
Format: Article
Published: Elsevier BV 2021
Online Access:http://psasir.upm.edu.my/id/eprint/95324/
https://www.sciencedirect.com/science/article/pii/S266672072100014X?via%3Dihub
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spelling my.upm.eprints.953242023-02-02T09:01:48Z http://psasir.upm.edu.my/id/eprint/95324/ Testing of linear models for optimal control of second-order dynamical system based on model-reality differences Kek, Sie Long Sim, Sy Yi Chen, Chuei Yee In this paper, the testing of linear models with different parameter values is conducted for solving the optimal control problem of a second-order dynamical system. The purpose of this testing is to provide the solution with the same structure but different parameter values in the model used. For doing so, the adjusted parameters are added to each model in order to measure the differences between the model used and the plant dynamics. On this basis, an expanded optimal control problem, which combines system optimization and parameter estimation, is introduced. Then, the Hamiltonian function is defined and a set of the necessary conditions is derived. Consequently, a modified model-based optimal control problem has resulted. Follow from this, an equivalent optimization problem without constraints is formulated. During the calculation procedure, the conjugate gradient algorithm is employed to solve the optimization problem, in turn, to update the adjusted parameters repeatedly for obtaining the optimal solution of the model used. Within a given tolerance, the iterative solution of the model used approximates the correct optimal solution of the original linear optimal control problem despite model-reality differences. The results obtained show the applicability of models with the same structures and different parameter values for solving the original linear optimal control problem. In conclusion, the efficiency of the approach proposed is highly verified. Elsevier BV 2021 Article PeerReviewed Kek, Sie Long and Sim, Sy Yi and Chen, Chuei Yee (2021) Testing of linear models for optimal control of second-order dynamical system based on model-reality differences. Results in Control and Optimization, 4. pp. 1-12. ISSN 2666-7207 https://www.sciencedirect.com/science/article/pii/S266672072100014X?via%3Dihub 10.1016/j.rico.2021.100022
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
description In this paper, the testing of linear models with different parameter values is conducted for solving the optimal control problem of a second-order dynamical system. The purpose of this testing is to provide the solution with the same structure but different parameter values in the model used. For doing so, the adjusted parameters are added to each model in order to measure the differences between the model used and the plant dynamics. On this basis, an expanded optimal control problem, which combines system optimization and parameter estimation, is introduced. Then, the Hamiltonian function is defined and a set of the necessary conditions is derived. Consequently, a modified model-based optimal control problem has resulted. Follow from this, an equivalent optimization problem without constraints is formulated. During the calculation procedure, the conjugate gradient algorithm is employed to solve the optimization problem, in turn, to update the adjusted parameters repeatedly for obtaining the optimal solution of the model used. Within a given tolerance, the iterative solution of the model used approximates the correct optimal solution of the original linear optimal control problem despite model-reality differences. The results obtained show the applicability of models with the same structures and different parameter values for solving the original linear optimal control problem. In conclusion, the efficiency of the approach proposed is highly verified.
format Article
author Kek, Sie Long
Sim, Sy Yi
Chen, Chuei Yee
spellingShingle Kek, Sie Long
Sim, Sy Yi
Chen, Chuei Yee
Testing of linear models for optimal control of second-order dynamical system based on model-reality differences
author_facet Kek, Sie Long
Sim, Sy Yi
Chen, Chuei Yee
author_sort Kek, Sie Long
title Testing of linear models for optimal control of second-order dynamical system based on model-reality differences
title_short Testing of linear models for optimal control of second-order dynamical system based on model-reality differences
title_full Testing of linear models for optimal control of second-order dynamical system based on model-reality differences
title_fullStr Testing of linear models for optimal control of second-order dynamical system based on model-reality differences
title_full_unstemmed Testing of linear models for optimal control of second-order dynamical system based on model-reality differences
title_sort testing of linear models for optimal control of second-order dynamical system based on model-reality differences
publisher Elsevier BV
publishDate 2021
url http://psasir.upm.edu.my/id/eprint/95324/
https://www.sciencedirect.com/science/article/pii/S266672072100014X?via%3Dihub
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score 13.209306