# Concurrent learning for parameter estimation using dynamic state-derivative estimators

arXiv: https://arxiv.org/abs/1507.08903 · HTML: https://mlsanity.com/paper/1507.08903/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jul 2015.

## Built on by (most cited first, 7 of 7)

- [System Identification and Control Using Lyapunov-Based Deep Neural Networks without Persistent Excitation: A Concurrent Learning Approach](https://mlsanity.com/paper/2505.10678/) (2025)
- [Online inverse reinforcement learning for nonlinear systems](https://mlsanity.com/paper/1811.10471/) (2018)
- [Concurrent Learning Based Tracking Control of Nonlinear Systems using Gaussian Process](https://mlsanity.com/paper/2106.00910/) (2021)
- [Nonlinear Discrete-time System Identification without Persistence of Excitation: Finite-time Concurrent Learning Methods](https://mlsanity.com/paper/2112.07765/) (2021)
- [Partial Excitation in Parameter Learning](https://mlsanity.com/paper/2503.02235/) (2025)
- [PACE: A Framework for Learning and Control in Linear Incomplete-Information Differential Games](https://mlsanity.com/paper/2504.17128/) (2025)
- [Neural ODEs Meet Concurrent Learning: Stable Online Learning with Lyapunov Guarantees](https://mlsanity.com/paper/2609.32289/) (2026)

## Abstract (arXiv)

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.