On Convergence of the Iteratively Preconditioned Gradient-Descent (IPG) Observer
<|reference_start|>On Convergence of the Iteratively Preconditioned Gradient-Descent (IPG) Observer: 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.<|reference_end|>
@article{chakrabarti2024on,
    title={On Convergence of the Iteratively Preconditioned Gradient-Descent (IPG)
  Observer},
    author={Kushal Chakrabarti, Nikhil Chopra},
    journal={IEEE Control Systems Letters, vol. 8, pp. 1715-1720, 2024},
    year={2024},
    doi={10.1109/LCSYS.2024.3416337},
    archivePrefix={arXiv},
    eprint={2405.09137},
    primaryClass={math.OC cs.SY eess.SY}
}