Dynamic Mode Decomposition of Control-Affine Nonlinear Systems using Discrete Control Liouville Operators
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929196361580544 |
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| author | Morrison, Zachary Abudia, Moad Rosenfeld, Joel Kamalapurar, Rushikesh |
| author_facet | Morrison, Zachary Abudia, Moad Rosenfeld, Joel Kamalapurar, Rushikesh |
| contents | Representation of nonlinear dynamical systems as infinite-dimensional linear operators over Hilbert spaces enables analysis of nonlinear systems via pseudo-spectral operator analysis. In this paper, we provide a novel representation for discrete-time control-affine nonlinear dynamical systems as linear operators acting on a Hilbert space. We also demonstrate that this representation can be used to predict the behavior of the closed-loop system given a known feedback law using recorded snapshots of the system state resulting from arbitrary, potentially open-loop control inputs. We thereby extend the predictive capabilities of dynamic mode decomposition to discrete-time nonlinear systems that are affine in control. We validate the method using two numerical experiments by predicting the response of a controlled Duffing oscillator to a known feedback law, as well as demonstrating the advantage of the developed method relative to existing techniques in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09817 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Dynamic Mode Decomposition of Control-Affine Nonlinear Systems using Discrete Control Liouville Operators Morrison, Zachary Abudia, Moad Rosenfeld, Joel Kamalapurar, Rushikesh Optimization and Control Dynamical Systems Functional Analysis Representation of nonlinear dynamical systems as infinite-dimensional linear operators over Hilbert spaces enables analysis of nonlinear systems via pseudo-spectral operator analysis. In this paper, we provide a novel representation for discrete-time control-affine nonlinear dynamical systems as linear operators acting on a Hilbert space. We also demonstrate that this representation can be used to predict the behavior of the closed-loop system given a known feedback law using recorded snapshots of the system state resulting from arbitrary, potentially open-loop control inputs. We thereby extend the predictive capabilities of dynamic mode decomposition to discrete-time nonlinear systems that are affine in control. We validate the method using two numerical experiments by predicting the response of a controlled Duffing oscillator to a known feedback law, as well as demonstrating the advantage of the developed method relative to existing techniques in the literature. |
| title | Dynamic Mode Decomposition of Control-Affine Nonlinear Systems using Discrete Control Liouville Operators |
| topic | Optimization and Control Dynamical Systems Functional Analysis |
| url | https://arxiv.org/abs/2309.09817 |