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Hopfield neural networks for on-line parameter estimation
Hugo Alonso1, Teresa Mendonça, Paula Rocha
1Unidade de Investigação Matemática e Aplicações, Universidade de Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal. hugo.alonso@ua.pt
Summary
This study enhances Hopfield Neural Networks (HNNs) for real-time parameter estimation. HNNs provide accurate, robust estimates even with system perturbations, outperforming other methods in case studies.
Area of Science:
- Artificial Intelligence
- Control Systems
- Dynamical Systems
Background:
- Hopfield Neural Networks (HNNs) are complex dynamical systems.
- On-line parameter estimation is crucial for real-time system adaptation.
- Existing HNN applications for parameter estimation have limitations.
Purpose of the Study:
- To investigate the efficacy of Hopfield Neural Networks (HNNs) for on-line parameter estimation.
- To analyze the stability and robustness of HNNs under generalized conditions.
- To compare HNN performance against alternative estimation methods.
Main Methods:
- Utilizing HNNs as nonautonomous nonlinear dynamical systems for time-evolving parameter estimation.
- Conducting stability analysis under more general assumptions than previously established.
- Performing robustness analysis to evaluate performance under perturbations.
- Illustrating results through two comparative case studies.
Main Results:
- A weaker sufficient condition for asymptotic convergence of estimation error to zero was derived.
- HNNs demonstrate robustness, with estimation error converging to a bounded neighborhood of zero.
- The size of the perturbation-induced error bound is inversely proportional to perturbation magnitude.
- HNNs showed competitive or superior performance compared to two other methods in case studies.
Conclusions:
- The proposed HNN approach offers a stable and robust method for on-line parameter estimation.
- The derived stability condition is less restrictive, broadening HNN applicability.
- HNNs provide reliable parameter estimates even in the presence of system noise or disturbances.
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