Sufficient Conditions for Persistency of Excitation with Step and ReLU Activation Functions

TL;DR

This paper establishes geometric criteria to ensure persistency of excitation in neural networks with step or ReLU activations, crucial for parameter convergence in adaptive control systems.

Contribution

It introduces new geometric conditions that guarantee persistency of excitation for neural networks with specific activation functions, linking them to adaptive control applications.

Findings

Conditions hold during reference system tracking

Parameter estimates converge to true values

Numerical validation confirms theoretical results

Abstract

This paper defines geometric criteria which are then used to establish sufficient conditions for persistency of excitation with vector functions constructed from single hidden-layer neural networks with step or ReLU activation functions. We show that these conditions hold when employing reference system tracking, as is commonly done in adaptive control. We demonstrate the results numerically on a system with linearly parameterized activations of this type and show that the parameter estimates converge to the true values with the sufficient conditions met.