Externally Recurrent Neural Network based identification of dynamic systems using Lyapunov stability analysis

Area of Science:

• * Computational neuroscience
• * Nonlinear dynamics
• * Machine learning

Background:

• * Complex nonlinear systems and time series present significant modeling challenges.
• * Existing methods may struggle with accurately approximating unknown system dynamics.
• * Accurate prediction is crucial in various scientific and engineering domains.

Purpose of the Study:

• * To propose a novel Externally Recurrent Neural Network (ERNN) for approximating complex nonlinear system dynamics.
• * To enable accurate time series prediction using the proposed ERNN model.
• * To rigorously analyze the stability and convergence properties of the ERNN.

Main Methods:

• * Development of an Externally Recurrent Neural Network (ERNN) architecture.
• * Utilization of present and delayed system outputs and external inputs.
• * Application of Lyapunov stability methods for weight update boundedness analysis.
• * Mathematical proof of error convergence.

Main Results:

• * The ERNN effectively approximates the dynamics of various nonlinear systems.
• * Performance evaluation demonstrates the ERNN's efficiency and accuracy.
• * Comparative analysis shows competitive or superior results against state-of-the-art methods.

Conclusions:

• * The proposed ERNN is an efficient and accurate method for nonlinear system dynamics approximation.
• * The ERNN shows significant potential for advanced time series prediction tasks.
• * Stability and convergence proofs provide theoretical validation for the model's reliability.