New optimal observer design for a class of nonlinear systems based on approximation

Kashefi, Saeed; Hajatipour, Majid

doi:10.1007/s40435-022-00979-5

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2024

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“…There is a vast literature of other classes of nonlinear observers, including [7]- [16]. A few notable ones are the exact linearization-based [7], [8], high-gain observers [9], [10], and qDES observer framework [11].…”

Section: Introductionmentioning

confidence: 99%

Robustness of Iteratively Pre-Conditioned Gradient-Descent Method: The Case of Distributed Linear Regression Problem

Chakrabarti

Gupta

Chopra

2021

2021 American Control Conference (ACC)

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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 Newtontype 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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