# Data-Guided Regulator for Adaptive Nonlinear Control

arXiv: https://arxiv.org/abs/2311.12230 · HTML: https://mlsanity.com/paper/2311.12230/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 30 references that are in the map.
- First posted on arXiv 20 Nov 2023.

## Builds on (most cited first, 13 of 13)

- [Learning agile and dynamic motor skills for legged robots](https://mlsanity.com/paper/1901.08652/) (2019)
- [Reinforcement Learning in Feature Space: Matrix Bandit, Kernels, and Regret Bound](https://mlsanity.com/paper/1905.10389/) (2019)
- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [Information Theoretic Regret Bounds for Online Nonlinear Control](https://mlsanity.com/paper/2006.12466/) (2020)
- [Neural-Fly Enables Rapid Learning for Agile Flight in Strong Winds](https://mlsanity.com/paper/2205.06908/) (2022)
- [Logarithmic Regret Bound in Partially Observable Linear Dynamical Systems](https://mlsanity.com/paper/2003.11227/) (2020)
- [Online Optimal Control with Linear Dynamics and Predictions: Algorithms and Regret Analysis](https://mlsanity.com/paper/1906.11378/) (2019)
- [The Power of Predictions in Online Control](https://mlsanity.com/paper/2006.07569/) (2020)
- [Regret Bounds for Adaptive Nonlinear Control](https://mlsanity.com/paper/2011.13101/) (2020)
- [Perturbation-based Regret Analysis of Predictive Control in Linear Time Varying Systems](https://mlsanity.com/paper/2106.10497/) (2021)
- [Meta-Adaptive Nonlinear Control: Theory and Algorithms](https://mlsanity.com/paper/2106.06098/) (2021)
- [Dual Quaternion Based Powered Descent Guidance with State-Triggered Constraints](https://mlsanity.com/paper/1904.09248/) (2019)
- [On Regularizability and its Application to Online Control of Unstable LTI Systems](https://mlsanity.com/paper/2006.00125/) (2020)

## Abstract (arXiv)

This paper addresses the problem of designing a data-driven feedback controller for complex nonlinear dynamical systems in the presence of time-varying disturbances with unknown dynamics. Such disturbances are modeled as the "unknown" part of the system dynamics. The goal is to achieve finite-time regulation of system states through direct policy updates while also generating informative data that can subsequently be used for data-driven stabilization or system identification. First, we expand upon the notion of "regularizability" and characterize this system characteristic for a linear time-varying representation of the nonlinear system with locally-bounded higher-order terms. "Rapid-regularizability" then gauges the extent by which a system can be regulated in finite time, in contrast to its asymptotic behavior. We then propose the Data-Guided Regulation for Adaptive Nonlinear Control ( DG-RAN) algorithm, an online iterative synthesis procedure that utilizes discrete time-series data from a single trajectory for regulating system states and identifying disturbance dynamics. The effectiveness of our approach is demonstrated on a 6-DOF power descent guidance problem in the presence of adverse environmental disturbances.