Consistency analysis of refined instrumental variable methods for continuous-time system identification in closed-loop
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914753670021120 |
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| author | González, Rodrigo A. Pan, Siqi Rojas, Cristian R. Welsh, James S. |
| author_facet | González, Rodrigo A. Pan, Siqi Rojas, Cristian R. Welsh, James S. |
| contents | Refined instrumental variable methods have been broadly used for identification of continuous-time systems in both open and closed-loop settings. However, the theoretical properties of these methods are still yet to be fully understood when operating in closed-loop. In this paper, we address the consistency of the simplified refined instrumental variable method for continuous-time systems (SRIVC) and its closed-loop variant CLSRIVC when they are applied on data that is generated from a feedback loop. In particular, we consider feedback loops consisting of continuous-time controllers, as well as the discrete-time control case. This paper proves that the SRIVC and CLSRIVC estimators are not generically consistent when there is a continuous-time controller in the loop, and that generic consistency can be achieved when the controller is implemented in discrete-time. Numerical simulations are presented to support the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_08955 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Consistency analysis of refined instrumental variable methods for continuous-time system identification in closed-loop González, Rodrigo A. Pan, Siqi Rojas, Cristian R. Welsh, James S. Systems and Control Refined instrumental variable methods have been broadly used for identification of continuous-time systems in both open and closed-loop settings. However, the theoretical properties of these methods are still yet to be fully understood when operating in closed-loop. In this paper, we address the consistency of the simplified refined instrumental variable method for continuous-time systems (SRIVC) and its closed-loop variant CLSRIVC when they are applied on data that is generated from a feedback loop. In particular, we consider feedback loops consisting of continuous-time controllers, as well as the discrete-time control case. This paper proves that the SRIVC and CLSRIVC estimators are not generically consistent when there is a continuous-time controller in the loop, and that generic consistency can be achieved when the controller is implemented in discrete-time. Numerical simulations are presented to support the theoretical results. |
| title | Consistency analysis of refined instrumental variable methods for continuous-time system identification in closed-loop |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2404.08955 |