On Convergence of the Iteratively Preconditioned Gradient-Descent (IPG) Observer
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913565185671168 |
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| author | Chakrabarti, Kushal Chopra, Nikhil |
| author_facet | Chakrabarti, Kushal Chopra, Nikhil |
| contents | This paper considers the observer design problem for discrete-time nonlinear dynamical systems with sampled measurement data. Earlier, the recently proposed Iteratively Preconditioned Gradient-Descent (IPG) observer, a Newton-type observer, has been empirically shown to have improved robustness against measurement noise than the prominent nonlinear observers, a property that other Newton-type observers lack. However, no theoretical guarantees on the convergence of the IPG observer were provided. This paper presents a rigorous convergence analysis of the IPG observer for a class of nonlinear systems in deterministic settings, proving its local linear convergence to the actual trajectory. Our assumptions are standard in the existing literature of Newton-type observers, and the analysis further confirms the relation of the IPG observer with the Newton observer, which was only hypothesized earlier. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09137 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Convergence of the Iteratively Preconditioned Gradient-Descent (IPG) Observer Chakrabarti, Kushal Chopra, Nikhil Optimization and Control Systems and Control This paper considers the observer design problem for discrete-time nonlinear dynamical systems with sampled measurement data. Earlier, the recently proposed Iteratively Preconditioned Gradient-Descent (IPG) observer, a Newton-type observer, has been empirically shown to have improved robustness against measurement noise than the prominent nonlinear observers, a property that other Newton-type observers lack. However, no theoretical guarantees on the convergence of the IPG observer were provided. This paper presents a rigorous convergence analysis of the IPG observer for a class of nonlinear systems in deterministic settings, proving its local linear convergence to the actual trajectory. Our assumptions are standard in the existing literature of Newton-type observers, and the analysis further confirms the relation of the IPG observer with the Newton observer, which was only hypothesized earlier. |
| title | On Convergence of the Iteratively Preconditioned Gradient-Descent (IPG) Observer |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2405.09137 |