Relationship Between Persistent Excitation Levels and RBF Network Structures, With Application to Performance...

Area of Science:

• Control Theory
• Machine Learning
• Nonlinear System Identification

Background:

• Deterministic learning theory for nonlinear systems utilizes Radial Basis Function (RBF) networks.
• Persistent excitation (PE) is a crucial concept for ensuring effective learning in these systems.
• Understanding the relationship between RBF network structure and PE is essential for performance analysis.

Purpose of the Study:

• To investigate the relationship between persistent excitation (PE) levels and Radial Basis Function (RBF) network structures.
• To determine how RBF network construction influences deterministic learning performance.
• To provide explicit formulas for PE levels based on RBF network density.

Main Methods:

• Analyzing state trajectories from nonlinear dynamical systems.
• Developing explicit formulas to quantify PE levels concerning RBF network center density.
• Applying these formulas to the convergence analysis of deterministic learning algorithms.

Main Results:

• PE levels decrease as the density of RBF network centers increases, as shown by derived formulas.
• A finite number of RBF centers can achieve the same deterministic learning performance as an infinite (global) set.
• A trade-off exists between high excitation levels and RBF network approximation accuracy.

Conclusions:

• The study provides a novel perspective on RBF network algorithm performance analysis through the lens of PE.
• Optimal RBF network design involves balancing center density for sufficient PE and approximation capabilities.
• Findings suggest that increasing RBF center density does not always guarantee improved convergence accuracy.