Koopman-based feedback design with stability guarantees
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913638355304448 |
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| author | Strässer, Robin Schaller, Manuel Worthmann, Karl Berberich, Julian Allgöwer, Frank |
| author_facet | Strässer, Robin Schaller, Manuel Worthmann, Karl Berberich, Julian Allgöwer, Frank |
| contents | We present a method to design a state-feedback controller ensuring exponential stability for nonlinear systems using only measurement data. Our approach relies on Koopman-operator theory and uses robust control to explicitly account for approximation errors due to finitely many data samples. To simplify practical usage across various applications, we provide a tutorial-style exposition of the feedback design and its stability guarantees for single-input systems. Moreover, we extend this controller design to multi-input systems and more flexible nonlinear state-feedback controllers using gain-scheduling techniques to increase the guaranteed region of attraction. As the proposed controller design is framed as a semidefinite program, it allows for an efficient solution. Further, we enhance the geometry of the region of attraction through a heuristic algorithm that establishes a connection between the employed Koopman lifting and the dynamics of the system. Finally, we validate the proposed feedback design procedure by means of numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_01441 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Koopman-based feedback design with stability guarantees Strässer, Robin Schaller, Manuel Worthmann, Karl Berberich, Julian Allgöwer, Frank Systems and Control Optimization and Control We present a method to design a state-feedback controller ensuring exponential stability for nonlinear systems using only measurement data. Our approach relies on Koopman-operator theory and uses robust control to explicitly account for approximation errors due to finitely many data samples. To simplify practical usage across various applications, we provide a tutorial-style exposition of the feedback design and its stability guarantees for single-input systems. Moreover, we extend this controller design to multi-input systems and more flexible nonlinear state-feedback controllers using gain-scheduling techniques to increase the guaranteed region of attraction. As the proposed controller design is framed as a semidefinite program, it allows for an efficient solution. Further, we enhance the geometry of the region of attraction through a heuristic algorithm that establishes a connection between the employed Koopman lifting and the dynamics of the system. Finally, we validate the proposed feedback design procedure by means of numerical examples. |
| title | Koopman-based feedback design with stability guarantees |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2312.01441 |