Concurrent learning for parameter estimation using dynamic state-derivative estimators

TL;DR

This paper introduces a novel concurrent learning parameter estimator for nonlinear systems that uses a dynamic state-derivative estimator and a purging algorithm, ensuring convergence without relying on state-derivative knowledge.

Contribution

It presents a new CL-based parameter estimation method with a dynamic derivative estimator and a purging algorithm, addressing limitations of existing techniques.

Findings

Converges asymptotically under persistent excitation.

Ensures bounded errors under finite excitation.

Demonstrates effectiveness through simulations.

Abstract

A concurrent learning (CL)-based parameter estimator is developed to identify the unknown parameters in a linearly parameterized uncertain control-affine nonlinear system. Unlike state-of-the-art CL techniques that assume knowledge of the state-derivative or rely on numerical smoothing, CL is implemented using a dynamic state-derivative estimator. A novel purging algorithm is introduced to discard possibly erroneous data recorded during the transient phase for concurrent learning. Since purging results in a discontinuous parameter adaptation law, the closed-loop error system is modeled as a switched system. Asymptotic convergence of the error states to the origin is established under a persistent excitation condition, and the error states are shown to be ultimately bounded under a finite excitation condition. Simulation results are provided to demonstrate the effectiveness of the developed parameter estimator.