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A gradient algorithm for optimal control problems with model-reality differences

In this paper, we propose a computational approach to solve a model-based optimal control problem. Our aim is to obtain the optimal so- lution of the nonlinear optimal control problem. Since the structures of both problems are different, only solving the model-based optimal control problem will not...

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Main Authors: Sie, Long Kek, Abd. Aziz, Mohd. Ismail, Kok, Lay Teo
Format: Article
Published: American Institute of Mathematical Sciences 2015
Subjects:
QA Mathematics
Online Access:http://eprints.utm.my/id/eprint/55464/
http://dx.doi.org/10.3934/naco.2015.3.251
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spelling my.utm.554642017-08-08T08:16:31Z http://eprints.utm.my/id/eprint/55464/ A gradient algorithm for optimal control problems with model-reality differences Sie, Long Kek Abd. Aziz, Mohd. Ismail Kok, Lay Teo QA Mathematics In this paper, we propose a computational approach to solve a model-based optimal control problem. Our aim is to obtain the optimal so- lution of the nonlinear optimal control problem. Since the structures of both problems are different, only solving the model-based optimal control problem will not give the optimal solution of the nonlinear optimal control problem. In our approach, the adjusted parameters are added into the model used so as the differences between the real plant and the model can be measured. On this basis, an expanded optimal control problem is introduced, where sys- tem optimization and parameter estimation are integrated interactively. The Hamiltonian function, which adjoins the cost function, the state equation and the additional constraints, is defined. By applying the calculus of variation, a set of the necessary optimality conditions, which defines modified model-based optimal control problem, parameter estimation problem and computation of modifiers, is then derived. To obtain the optimal solution, the modified model- based optimal control problem is converted in a nonlinear programming prob- lem through the canonical formulation, where the gradient formulation can be made. During the iterative procedure, the control sequences are generated as the admissible control law of the model used, together with the corresponding state sequences. Consequently, the optimal solution is updated repeatedly by the adjusted parameters. At the end of iteration, the converged solution ap- proaches to the correct optimal solution of the original optimal control problem in spite of model-reality differences. American Institute of Mathematical Sciences 2015 Article PeerReviewed Sie, Long Kek and Abd. Aziz, Mohd. Ismail and Kok, Lay Teo (2015) A gradient algorithm for optimal control problems with model-reality differences. Numerical Algebra, Control and Optimization, 5 (3). pp. 251-266. ISSN 2155-3289 http://dx.doi.org/10.3934/naco.2015.3.251 DOI:10.3934/naco.2015.3.251
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
topic QA Mathematics
spellingShingle QA Mathematics
Sie, Long Kek
Abd. Aziz, Mohd. Ismail
Kok, Lay Teo
A gradient algorithm for optimal control problems with model-reality differences
description In this paper, we propose a computational approach to solve a model-based optimal control problem. Our aim is to obtain the optimal so- lution of the nonlinear optimal control problem. Since the structures of both problems are different, only solving the model-based optimal control problem will not give the optimal solution of the nonlinear optimal control problem. In our approach, the adjusted parameters are added into the model used so as the differences between the real plant and the model can be measured. On this basis, an expanded optimal control problem is introduced, where sys- tem optimization and parameter estimation are integrated interactively. The Hamiltonian function, which adjoins the cost function, the state equation and the additional constraints, is defined. By applying the calculus of variation, a set of the necessary optimality conditions, which defines modified model-based optimal control problem, parameter estimation problem and computation of modifiers, is then derived. To obtain the optimal solution, the modified model- based optimal control problem is converted in a nonlinear programming prob- lem through the canonical formulation, where the gradient formulation can be made. During the iterative procedure, the control sequences are generated as the admissible control law of the model used, together with the corresponding state sequences. Consequently, the optimal solution is updated repeatedly by the adjusted parameters. At the end of iteration, the converged solution ap- proaches to the correct optimal solution of the original optimal control problem in spite of model-reality differences.
format Article
author Sie, Long Kek
Abd. Aziz, Mohd. Ismail
Kok, Lay Teo
author_facet Sie, Long Kek
Abd. Aziz, Mohd. Ismail
Kok, Lay Teo
author_sort Sie, Long Kek
title A gradient algorithm for optimal control problems with model-reality differences
title_short A gradient algorithm for optimal control problems with model-reality differences
title_full A gradient algorithm for optimal control problems with model-reality differences
title_fullStr A gradient algorithm for optimal control problems with model-reality differences
title_full_unstemmed A gradient algorithm for optimal control problems with model-reality differences
title_sort gradient algorithm for optimal control problems with model-reality differences
publisher American Institute of Mathematical Sciences
publishDate 2015
url http://eprints.utm.my/id/eprint/55464/
http://dx.doi.org/10.3934/naco.2015.3.251
_version_ 1643653804857491456
score 13.244404

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