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arXiv · 2405.09137

On Convergence of the Iteratively Preconditioned Gradient-Descent (IPG) Observer

Kushal Chakrabarti·Nikhil Chopra
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Abstract

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.

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Kushal Chakrabarti, Nikhil Chopra. 2024-05-15. On Convergence of the Iteratively Preconditioned Gradient-Descent (IPG) Observer. https://doi.org/10.1109/lcsys.2024.3416337

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