Dynamic system identification based on a novel pi-sigma neural network with Lyapunov stability analysis

Area of Science:

• Artificial Intelligence
• Computational Neuroscience
• Dynamical Systems Theory

Background:

• Non-linear dynamical systems present significant modeling challenges.
• Existing neural network architectures have limitations in capturing complex dynamics.
• Pi-Sigma Neural Networks (PSNN) offer enhanced non-linear modeling capabilities.

Purpose of the Study:

• Introduce a novel recurrent neural network, the Diagonally Layered Pi-Sigma Neural Network (DLPSNN).
• Enhance the modeling of non-linear dynamical systems using DLPSNN.
• Evaluate the stability and robustness of the proposed DLPSNN model.

Main Methods:

• Developed DLPSNN by adapting the PSNN with additional feedback layers.
• Employed the Back Propagation (BP) algorithm for weight updates.
• Assessed model stability using Lyapunov-Stability (LS) principles.

Main Results:

• DLPSNN demonstrated superior performance in identifying non-linear dynamical systems.
• The model achieved higher output accuracy and minimized errors compared to PSNN, FNN, ENN, DNN, and JNN.
• DLPSNN exhibited robust recovery from perturbations.

Conclusions:

• The DLPSNN is a highly effective recurrent model for non-linear dynamical system identification.
• DLPSNN offers significant improvements in accuracy and robustness over existing neural network models.
• The model's stability and resilience make it suitable for complex real-world applications.