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arXiv · 2502.04551

Stability of Jordan Recurrent Neural Network Estimator

Avneet Kaur·Ruikun Zhou·Jun Liu·Kirsten Morris
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Abstract

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.

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Avneet Kaur, Ruikun Zhou, Jun Liu, Kirsten Morris. 2025-02-06. Stability of Jordan Recurrent Neural Network Estimator. https://arxiv.org/abs/2502.04551

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