Bridging Model Reference Adaptive Control and Data Informativity
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918385112055808 |
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| author | Wang, Jiwei Baldi, Simone van Waarde, Henk J. |
| author_facet | Wang, Jiwei Baldi, Simone van Waarde, Henk J. |
| contents | The goal of model reference adaptive control (MRAC) is to ensure that the trajectories of an unknown dynamical system track those of a given reference model. This is done by means of a feedback controller that adaptively changes its gains using data collected online from the closed-loop system. One of the approaches to solve the MRAC problem is to impose conditions on the data that guarantee convergence of the gains to a solution of the so-called matching equations. In the literature, various extensions of the concept of persistent excitation have been proposed in an effort to weaken the conditions on the data required for this convergence. Despite these efforts, it is not well-understood what conditions are necessary and sufficient for ensuring convergence of MRAC to a solution of the matching equations. In this paper, we propose a new framework to study the MRAC problem, using the concept of data informativity. Our main contribution is to provide \emph{necessary and sufficient} conditions for the existence of an adaptive law that guarantees convergence of the gains to a solution of the matching equations, and to provide a recipe for its construction. While existing excitation conditions imply that the system can be uniquely identified from the collected data, our results show that this is not necessary for the convergence of the feedback gains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_21091 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bridging Model Reference Adaptive Control and Data Informativity Wang, Jiwei Baldi, Simone van Waarde, Henk J. Optimization and Control The goal of model reference adaptive control (MRAC) is to ensure that the trajectories of an unknown dynamical system track those of a given reference model. This is done by means of a feedback controller that adaptively changes its gains using data collected online from the closed-loop system. One of the approaches to solve the MRAC problem is to impose conditions on the data that guarantee convergence of the gains to a solution of the so-called matching equations. In the literature, various extensions of the concept of persistent excitation have been proposed in an effort to weaken the conditions on the data required for this convergence. Despite these efforts, it is not well-understood what conditions are necessary and sufficient for ensuring convergence of MRAC to a solution of the matching equations. In this paper, we propose a new framework to study the MRAC problem, using the concept of data informativity. Our main contribution is to provide \emph{necessary and sufficient} conditions for the existence of an adaptive law that guarantees convergence of the gains to a solution of the matching equations, and to provide a recipe for its construction. While existing excitation conditions imply that the system can be uniquely identified from the collected data, our results show that this is not necessary for the convergence of the feedback gains. |
| title | Bridging Model Reference Adaptive Control and Data Informativity |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2502.21091 |