# Nonlinear Discrete-time System Identification without Persistence of Excitation: Finite-time Concurrent Learning Methods

arXiv: https://arxiv.org/abs/2112.07765 · HTML: https://mlsanity.com/paper/2112.07765/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 36 references that are in the map.
- First posted on arXiv 14 Dec 2021.

## Builds on (most cited first, 3 of 3)

- [Active Learning for Nonlinear System Identification with Guarantees](https://mlsanity.com/paper/2006.10277/) (2020)
- [Concurrent learning for parameter estimation using dynamic state-derivative estimators](https://mlsanity.com/paper/1507.08903/) (2015)
- [New Results on Parameter Estimation via Dynamic Regressor Extension and Mixing: Continuous and Discrete-time Cases](https://mlsanity.com/paper/1908.05125/) (2019)

## Abstract (arXiv)

This paper deals with the problem of finite-time learning for unknown discrete-time nonlinear systems' dynamics, without the requirement of the persistence of excitation. Two finite-time concurrent learning methods are presented to approximate the uncertainties of the discrete-time nonlinear systems in an online fashion by employing current data along with recorded experienced data satisfying an easy-to-check rank condition on the richness of the recorded data which is less restrictive in comparison with persistence of excitation condition. For the proposed finite-time concurrent learning methods, rigorous proofs guarantee the finite-time convergence of the estimated parameters to their optimal values based on the discrete-time Lyapunov analysis. Compared with the existing work in the literature, simulation results illustrate that the proposed methods can timely and precisely approximate the uncertainties.