# Concurrent Learning Based Tracking Control of Nonlinear Systems using Gaussian Process

arXiv: https://arxiv.org/abs/2106.00910 · HTML: https://mlsanity.com/paper/2106.00910/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 26 references that are in the map.
- First posted on arXiv 2 Jun 2021.

## Builds on (most cited first, 9 of 9)

- [Feedback Linearization based on Gaussian Processes with event-triggered Online Learning](https://mlsanity.com/paper/1911.06565/) (2019)
- [Stochastic data-driven model predictive control using Gaussian processes](https://mlsanity.com/paper/1908.01786/) (2019)
- [Concurrent learning for parameter estimation using dynamic state-derivative estimators](https://mlsanity.com/paper/1507.08903/) (2015)
- [Stable Gaussian Process based Tracking Control of Euler-Lagrange Systems](https://mlsanity.com/paper/1806.07190/) (2018)
- [Feedback Linearization for Unknown Systems via Reinforcement Learning](https://mlsanity.com/paper/1910.13272/) (2019)
- [Stable Gaussian Process based Tracking Control of Lagrangian Systems](https://mlsanity.com/paper/1811.07711/) (2018)
- [Closed-Loop Error Learning Control for Uncertain Nonlinear Systems With Experimental Validation on a Mobile Robot](https://mlsanity.com/paper/2103.08845/) (2021)
- [Sliding Mode Learning Control of Uncertain Nonlinear Systems with Lyapunov Stability Analysis](https://mlsanity.com/paper/2103.11274/) (2021)
- [Adaptive and Efficient Model Predictive Control for Booster Reentry](https://mlsanity.com/paper/2103.12536/) (2021)

## Abstract (arXiv)

This paper demonstrates the applicability of the combination of concurrent learning as a tool for parameter estimation and non-parametric Gaussian Process for online disturbance learning. A control law is developed by using both techniques sequentially in the context of feedback linearization. The concurrent learning algorithm estimates the system parameters of structured uncertainty without requiring persistent excitation, which are used in the design of the feedback linearization law. Then, a non-parametric Gaussian Process learns unstructured uncertainty. The closed-loop system stability for the nth-order system is proven using the Lyapunov stability theorem. The simulation results show that the tracking error is minimized (i) when true values of model parameters have not been provided, (ii) in the presence of disturbances introduced once the parameters have converged to their true values and (iii) when system parameters have not converged to their true values in the presence of disturbances.