The Euler-Lagrange equation and optimal control: Preliminary results
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866909343263227904 |
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| author | Join, Cédric Delaleau, Emmanuel Fliess, Michel |
| author_facet | Join, Cédric Delaleau, Emmanuel Fliess, Michel |
| contents | Algebraically speaking, linear time-invariant (LTI) systems can be considered as modules. In this framework, controllability is translated as the freeness of the system module. Optimal control mainly relies on quadratic Lagrangians and the consideration of any basis of the system module leads to an open-loop control strategy via a linear Euler-Lagrange equation. In this approach, the endpoint is easily assignable and time horizon can be chosen to minimize the criterion. The loop is closed via an intelligent controller derived from model-free control, which exhibits excellent performances concerning model mismatches and disturbances. The extension to nonlinear systems is briefly discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07040 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Euler-Lagrange equation and optimal control: Preliminary results Join, Cédric Delaleau, Emmanuel Fliess, Michel Optimization and Control Systems and Control 49J15, 49N10 Algebraically speaking, linear time-invariant (LTI) systems can be considered as modules. In this framework, controllability is translated as the freeness of the system module. Optimal control mainly relies on quadratic Lagrangians and the consideration of any basis of the system module leads to an open-loop control strategy via a linear Euler-Lagrange equation. In this approach, the endpoint is easily assignable and time horizon can be chosen to minimize the criterion. The loop is closed via an intelligent controller derived from model-free control, which exhibits excellent performances concerning model mismatches and disturbances. The extension to nonlinear systems is briefly discussed. |
| title | The Euler-Lagrange equation and optimal control: Preliminary results |
| topic | Optimization and Control Systems and Control 49J15, 49N10 |
| url | https://arxiv.org/abs/2410.07040 |