Two Roads to Koopman Operator Theory for Control: Infinite Input Sequences and Operator Families
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914098004885504 |
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| author | Haseli, Masih Mezić, Igor Cortés, Jorge |
| author_facet | Haseli, Masih Mezić, Igor Cortés, Jorge |
| contents | The Koopman operator, originally defined for dynamical systems without input, has inspired many applications in control. Yet, the theoretical foundations underpinning this progress in control remain underdeveloped. This paper investigates the theoretical structure and connections between two extensions of Koopman theory to control: (i) Koopman operator via infinite input sequences and (ii) the Koopman control family. Although these frameworks encode system information in fundamentally different ways, we show that under certain conditions on the function spaces they operate on, they are equivalent. The equivalence is both in terms of the actions of the Koopman-based formulations in each framework as well as the function values on the system trajectories. Our analysis provides constructive tools to translate between the frameworks, offering a unified perspective for Koopman methods in control. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15166 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two Roads to Koopman Operator Theory for Control: Infinite Input Sequences and Operator Families Haseli, Masih Mezić, Igor Cortés, Jorge Optimization and Control Systems and Control Dynamical Systems The Koopman operator, originally defined for dynamical systems without input, has inspired many applications in control. Yet, the theoretical foundations underpinning this progress in control remain underdeveloped. This paper investigates the theoretical structure and connections between two extensions of Koopman theory to control: (i) Koopman operator via infinite input sequences and (ii) the Koopman control family. Although these frameworks encode system information in fundamentally different ways, we show that under certain conditions on the function spaces they operate on, they are equivalent. The equivalence is both in terms of the actions of the Koopman-based formulations in each framework as well as the function values on the system trajectories. Our analysis provides constructive tools to translate between the frameworks, offering a unified perspective for Koopman methods in control. |
| title | Two Roads to Koopman Operator Theory for Control: Infinite Input Sequences and Operator Families |
| topic | Optimization and Control Systems and Control Dynamical Systems |
| url | https://arxiv.org/abs/2510.15166 |