Reduced-order Koopman modeling and predictive control of nonlinear processes
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866913292818055168 |
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| author | Zhang, Xuewen Han, Minghao Yin, Xunyuan |
| author_facet | Zhang, Xuewen Han, Minghao Yin, Xunyuan |
| contents | In this paper, we propose an efficient data-driven predictive control approach for general nonlinear processes based on a reduced-order Koopman operator. A Kalman-based sparse identification of nonlinear dynamics method is employed to select lifting functions for Koopman identification. The selected lifting functions are used to project the original nonlinear state-space into a higher-dimensional linear function space, in which Koopman-based linear models can be constructed for the underlying nonlinear process. To curb the significant increase in the dimensionality of the resulting full-order Koopman models caused by the use of lifting functions, we propose a reduced-order Koopman modeling approach based on proper orthogonal decomposition. A computationally efficient linear robust predictive control scheme is established based on the reduced-order Koopman model. A case study on a benchmark chemical process is conducted to illustrate the effectiveness of the proposed method. Comprehensive comparisons are conducted to demonstrate the advantage of the proposed method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00553 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reduced-order Koopman modeling and predictive control of nonlinear processes Zhang, Xuewen Han, Minghao Yin, Xunyuan Systems and Control In this paper, we propose an efficient data-driven predictive control approach for general nonlinear processes based on a reduced-order Koopman operator. A Kalman-based sparse identification of nonlinear dynamics method is employed to select lifting functions for Koopman identification. The selected lifting functions are used to project the original nonlinear state-space into a higher-dimensional linear function space, in which Koopman-based linear models can be constructed for the underlying nonlinear process. To curb the significant increase in the dimensionality of the resulting full-order Koopman models caused by the use of lifting functions, we propose a reduced-order Koopman modeling approach based on proper orthogonal decomposition. A computationally efficient linear robust predictive control scheme is established based on the reduced-order Koopman model. A case study on a benchmark chemical process is conducted to illustrate the effectiveness of the proposed method. Comprehensive comparisons are conducted to demonstrate the advantage of the proposed method. |
| title | Reduced-order Koopman modeling and predictive control of nonlinear processes |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2404.00553 |