Concurrent learning in high-order tuners for parameter identification

TL;DR

This paper introduces a novel concurrent learning approach for high-order tuners that relaxes persistent excitation requirements, enhances efficiency, and maintains stability through reset methods, benefiting parameter identification tasks.

Contribution

It develops a new stability analysis for high-order tuners using Matrosov theorem and introduces a concurrent learning technique that relaxes PE conditions.

Findings

Concurrent learning significantly improves efficiency.

Reset methods preserve stability while enhancing accuracy.

Numerical results demonstrate practical benefits.

Abstract

High-order tuners are algorithms that show promise in achieving greater efficiency than classic gradient-based algorithms in identifying the parameters of parametric models and/or in facilitating the progress of a control or optimization algorithm whose adaptive behavior relies on such models. For high-order tuners, robust stability properties, namely uniform global asymptotic (and exponential) stability, currently rely on a persistent excitation (PE) condition. In this work, we establish such stability properties with a novel analysis based on a Matrosov theorem and then show that the PE requirement can be relaxed via a concurrent learning technique driven by sampled data points that are sufficiently rich. We show numerically that concurrent learning may greatly improve efficiency. We incorporate reset methods that preserve the stability guarantees while providing additional improvements that may be relevant in applications that demand highly accurate parameter estimates at relatively low additional cost in computation.