Stability of Jordan Recurrent Neural Network Estimator

Fuente: arXiv
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Autori principali: Kaur, Avneet, Zhou, Ruikun, Liu, Jun, Morris, Kirsten
Natura: Preprint
Pubblicazione: 2025
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author Kaur, Avneet
Zhou, Ruikun
Liu, Jun
Morris, Kirsten
author_facet Kaur, Avneet
Zhou, Ruikun
Liu, Jun
Morris, Kirsten
contents State estimation refers to determining the states of a dynamical system that starts from a noisy initial condition and evolves under process noise, based on noisy measurements and a known system model. For linear dynamical systems with white Gaussian noises of known mean and variance, Kalman filtering is a well-known method that leads to stable error dynamics for detectable systems. There are some non-optimal extensions to nonlinear systems. Recent work has used neural networks to develop estimators for nonlinear systems that optimize a criterion. Stability of the error dynamics is even more important than optimality. Jordan recurrent neural networks (JRNs) have a structure that mimics that of a dynamical system and are thus appealing for estimator design. We show that a JRN performs better than an extended Kalman filter(EKF) and unscented Kalman filter(UKF) for several examples. The main contribution of this paper is an input-to-state stability analysis of the error dynamics of JRNs. The stability of the error dynamics of several examples is shown.
format Preprint
id arxiv_https___arxiv_org_abs_2502_04551
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Stability of Jordan Recurrent Neural Network Estimator
Kaur, Avneet
Zhou, Ruikun
Liu, Jun
Morris, Kirsten
Optimization and Control
Dynamical Systems
State estimation refers to determining the states of a dynamical system that starts from a noisy initial condition and evolves under process noise, based on noisy measurements and a known system model. For linear dynamical systems with white Gaussian noises of known mean and variance, Kalman filtering is a well-known method that leads to stable error dynamics for detectable systems. There are some non-optimal extensions to nonlinear systems. Recent work has used neural networks to develop estimators for nonlinear systems that optimize a criterion. Stability of the error dynamics is even more important than optimality. Jordan recurrent neural networks (JRNs) have a structure that mimics that of a dynamical system and are thus appealing for estimator design. We show that a JRN performs better than an extended Kalman filter(EKF) and unscented Kalman filter(UKF) for several examples. The main contribution of this paper is an input-to-state stability analysis of the error dynamics of JRNs. The stability of the error dynamics of several examples is shown.
title Stability of Jordan Recurrent Neural Network Estimator
topic Optimization and Control
Dynamical Systems
url https://arxiv.org/abs/2502.04551