Exact Decomposition of Optimal Control Problems via Simultaneous Block Diagonalization of Matrices
In this paper, we consider optimal control problems (OCPs) applied to large-scale linear dynamical systems with a large number of states and inputs. We attempt to reduce such problems into a set of independent OCPs of lower dimensions. Our decomposition is ‘exact’ in the sense...
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| Format: | Article |
| Language: | English |
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IEEE
2023-01-01
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| Series: | IEEE Open Journal of Control Systems |
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| Online Access: | https://ieeexplore.ieee.org/document/9996568/ |
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| author | Amirhossein Nazerian Kshitij Bhatta Francesco Sorrentino |
| author_facet | Amirhossein Nazerian Kshitij Bhatta Francesco Sorrentino |
| author_sort | Amirhossein Nazerian |
| collection | DOAJ |
| description | In this paper, we consider optimal control problems (OCPs) applied to large-scale linear dynamical systems with a large number of states and inputs. We attempt to reduce such problems into a set of independent OCPs of lower dimensions. Our decomposition is ‘exact’ in the sense that it preserves all the information about the original system and the objective function. Previous work in this area has focused on strategies that exploit symmetries of the underlying system and of the objective function. Here, instead, we implement the algebraic method of simultaneous block diagonalization of matrices (SBD), which we show provides advantages both in terms of the dimension of the subproblems that are obtained and of the computation time. We provide practical examples with networked systems that demonstrate the benefits of applying the SBD decomposition over the decomposition method based on group symmetries. |
| first_indexed | 2024-03-13T03:49:57Z |
| format | Article |
| id | doaj.art-88daa563bef94ad5bbb44420f697fa80 |
| institution | Directory Open Access Journal |
| issn | 2694-085X |
| language | English |
| last_indexed | 2024-03-13T03:49:57Z |
| publishDate | 2023-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Open Journal of Control Systems |
| spelling | doaj.art-88daa563bef94ad5bbb44420f697fa802023-06-22T16:06:33ZengIEEEIEEE Open Journal of Control Systems2694-085X2023-01-012243510.1109/OJCSYS.2022.32315539996568Exact Decomposition of Optimal Control Problems via Simultaneous Block Diagonalization of MatricesAmirhossein Nazerian0https://orcid.org/0000-0003-1280-2353Kshitij Bhatta1https://orcid.org/0000-0002-7884-9667Francesco Sorrentino2https://orcid.org/0000-0001-8899-1176Mechanical Engineering Department, University of New Mexico, Albuquerque, NM, USAMechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA, USAMechanical Engineering Department, University of New Mexico, Albuquerque, NM, USAIn this paper, we consider optimal control problems (OCPs) applied to large-scale linear dynamical systems with a large number of states and inputs. We attempt to reduce such problems into a set of independent OCPs of lower dimensions. Our decomposition is ‘exact’ in the sense that it preserves all the information about the original system and the objective function. Previous work in this area has focused on strategies that exploit symmetries of the underlying system and of the objective function. Here, instead, we implement the algebraic method of simultaneous block diagonalization of matrices (SBD), which we show provides advantages both in terms of the dimension of the subproblems that are obtained and of the computation time. We provide practical examples with networked systems that demonstrate the benefits of applying the SBD decomposition over the decomposition method based on group symmetries.https://ieeexplore.ieee.org/document/9996568/Decouplingoptimal controlsimultaneous block diagonalization |
| spellingShingle | Amirhossein Nazerian Kshitij Bhatta Francesco Sorrentino Exact Decomposition of Optimal Control Problems via Simultaneous Block Diagonalization of Matrices IEEE Open Journal of Control Systems Decoupling optimal control simultaneous block diagonalization |
| title | Exact Decomposition of Optimal Control Problems via Simultaneous Block Diagonalization of Matrices |
| title_full | Exact Decomposition of Optimal Control Problems via Simultaneous Block Diagonalization of Matrices |
| title_fullStr | Exact Decomposition of Optimal Control Problems via Simultaneous Block Diagonalization of Matrices |
| title_full_unstemmed | Exact Decomposition of Optimal Control Problems via Simultaneous Block Diagonalization of Matrices |
| title_short | Exact Decomposition of Optimal Control Problems via Simultaneous Block Diagonalization of Matrices |
| title_sort | exact decomposition of optimal control problems via simultaneous block diagonalization of matrices |
| topic | Decoupling optimal control simultaneous block diagonalization |
| url | https://ieeexplore.ieee.org/document/9996568/ |
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