A new framework for solving fractional optimal control problems using fractional pseudospectral methods
The main purpose of this work is to provide new fractional pseudospectral methods for solving fractional optimal control problems (FOCPs). We develop differential and integral fractional pseudospectral methods and prove the equivalence between them from the distinctive perspective of Caputo fraction...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2017
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/85494 http://hdl.handle.net/10220/43729 |
| _version_ | 1811682737579360256 |
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| author | Shi, Yang Wang, Li-Lian Tang, Xiaojun |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Shi, Yang Wang, Li-Lian Tang, Xiaojun |
| author_sort | Shi, Yang |
| collection | NTU |
| description | The main purpose of this work is to provide new fractional pseudospectral methods for solving fractional optimal control problems (FOCPs). We develop differential and integral fractional pseudospectral methods and prove the equivalence between them from the distinctive perspective of Caputo fractional Birkhoff interpolation. As a result, the present work establishes a new unified framework for solving fractional optimal control problems using fractional pseudospectral methods, which can be viewed as an extension of existing frameworks. Furthermore, we provide exact, efficient, and stable approaches to compute the associated fractional pseudospectral differentiation/integration matrices even at millions of Jacobi-type points. Numerical results on two benchmark FOCPs including a fractional bang–bang problem demonstrate the performance of the proposed methods. |
| first_indexed | 2024-10-01T04:01:36Z |
| format | Journal Article |
| id | ntu-10356/85494 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T04:01:36Z |
| publishDate | 2017 |
| record_format | dspace |
| spelling | ntu-10356/854942020-03-07T12:31:31Z A new framework for solving fractional optimal control problems using fractional pseudospectral methods Shi, Yang Wang, Li-Lian Tang, Xiaojun School of Physical and Mathematical Sciences Optimal Control Pseudospectral Methods The main purpose of this work is to provide new fractional pseudospectral methods for solving fractional optimal control problems (FOCPs). We develop differential and integral fractional pseudospectral methods and prove the equivalence between them from the distinctive perspective of Caputo fractional Birkhoff interpolation. As a result, the present work establishes a new unified framework for solving fractional optimal control problems using fractional pseudospectral methods, which can be viewed as an extension of existing frameworks. Furthermore, we provide exact, efficient, and stable approaches to compute the associated fractional pseudospectral differentiation/integration matrices even at millions of Jacobi-type points. Numerical results on two benchmark FOCPs including a fractional bang–bang problem demonstrate the performance of the proposed methods. MOE (Min. of Education, S’pore) 2017-09-12T06:03:03Z 2019-12-06T16:04:51Z 2017-09-12T06:03:03Z 2019-12-06T16:04:51Z 2016 Journal Article Tang, X., Shi, Y., & Wang, L.-L. (2017). A new framework for solving fractional optimal control problems using fractional pseudospectral methods. Automatica, 78, 333-340. 0005-1098 https://hdl.handle.net/10356/85494 http://hdl.handle.net/10220/43729 10.1016/j.automatica.2016.12.022 en Automatica © 2016 Elsevier Ltd. |
| spellingShingle | Optimal Control Pseudospectral Methods Shi, Yang Wang, Li-Lian Tang, Xiaojun A new framework for solving fractional optimal control problems using fractional pseudospectral methods |
| title | A new framework for solving fractional optimal control problems using fractional pseudospectral methods |
| title_full | A new framework for solving fractional optimal control problems using fractional pseudospectral methods |
| title_fullStr | A new framework for solving fractional optimal control problems using fractional pseudospectral methods |
| title_full_unstemmed | A new framework for solving fractional optimal control problems using fractional pseudospectral methods |
| title_short | A new framework for solving fractional optimal control problems using fractional pseudospectral methods |
| title_sort | new framework for solving fractional optimal control problems using fractional pseudospectral methods |
| topic | Optimal Control Pseudospectral Methods |
| url | https://hdl.handle.net/10356/85494 http://hdl.handle.net/10220/43729 |
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