# Meta-Adaptive Nonlinear Control: Theory and Algorithms

arXiv: https://arxiv.org/abs/2106.06098 · HTML: https://mlsanity.com/paper/2106.06098/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 53 references that are in the map.
- First posted on arXiv 11 Jun 2021.

## Builds on (most cited first, 30 of 35)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Learning Quadrupedal Locomotion over Challenging Terrain](https://mlsanity.com/paper/2010.11251/) (2020)
- [Learning to Adapt in Dynamic, Real-World Environments Through Meta-Reinforcement Learning](https://mlsanity.com/paper/1803.11347/) (2018)
- [Meta-Learning: A Survey](https://mlsanity.com/paper/1810.03548/) (2018)
- [Few-Shot Learning via Learning the Representation, Provably](https://mlsanity.com/paper/2002.09434/) (2020)
- [DeepMDP: Learning Continuous Latent Space Models for Representation Learning](https://mlsanity.com/paper/1906.02736/) (2019)
- [The Benefit of Multitask Representation Learning](https://mlsanity.com/paper/1505.06279/) (2015)
- [On the Theory of Transfer Learning: The Importance of Task Diversity](https://mlsanity.com/paper/2006.11650/) (2020)
- [Adaptive Gradient-Based Meta-Learning Methods](https://mlsanity.com/paper/1906.02717/) (2019)
- [Provable Meta-Learning of Linear Representations](https://mlsanity.com/paper/2002.11684/) (2020)
- [On the Sample Complexity of the Linear Quadratic Regulator](https://mlsanity.com/paper/1710.01688/) (2017)
- [TossingBot: Learning to Throw Arbitrary Objects with Residual Physics](https://mlsanity.com/paper/1903.11239/) (2019)
- [Meta-Reinforcement Learning of Structured Exploration Strategies](https://mlsanity.com/paper/1802.07245/) (2018)
- [State Representation Learning for Control: An Overview](https://mlsanity.com/paper/1802.04181/) (2018)
- [Naive Exploration is Optimal for Online LQR](https://mlsanity.com/paper/2001.09576/) (2020)
- [Information Theoretic Regret Bounds for Online Nonlinear Control](https://mlsanity.com/paper/2006.12466/) (2020)
- [Neural Lander: Stable Drone Landing Control using Learned Dynamics](https://mlsanity.com/paper/1811.08027/) (2018)
- [Online Linear Quadratic Control](https://mlsanity.com/paper/1806.07104/) (2018)
- [Learning-to-Learn Stochastic Gradient Descent with Biased Regularization](https://mlsanity.com/paper/1903.10399/) (2019)
- [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)
- [Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems](https://mlsanity.com/paper/2103.04490/) (2021)
- [The Power of Predictions in Online Control](https://mlsanity.com/paper/2006.07569/) (2020)
- [Learning Causal State Representations of Partially Observable Environments](https://mlsanity.com/paper/1906.10437/) (2019)
- [Regret Bounds for Adaptive Nonlinear Control](https://mlsanity.com/paper/2011.13101/) (2020)
- [Robust Regression for Safe Exploration in Control](https://mlsanity.com/paper/1906.05819/) (2019)
- [Neural-Swarm: Decentralized Close-Proximity Multirotor Control Using Learned Interactions](https://mlsanity.com/paper/2003.02992/) (2020)

## Built on by (most cited first, 23 of 23)

- [Neural-Fly Enables Rapid Learning for Agile Flight in Strong Winds](https://mlsanity.com/paper/2205.06908/) (2022)
- [Multi-Task Imitation Learning for Linear Dynamical Systems](https://mlsanity.com/paper/2212.00186/) (2022)
- [Optimal Exploration for Model-Based RL in Nonlinear Systems](https://mlsanity.com/paper/2306.09210/) (2023)
- [Sample-Efficient Linear Representation Learning from Non-IID Non-Isotropic Data](https://mlsanity.com/paper/2308.04428/) (2023)
- [Improved Active Multi-Task Representation Learning via Lasso](https://mlsanity.com/paper/2306.02556/) (2023)
- [Safe Deep Policy Adaptation](https://mlsanity.com/paper/2310.08602/) (2023)
- [Constrained Meta-Reinforcement Learning for Adaptable Safety Guarantee with Differentiable Convex Programming](https://mlsanity.com/paper/2312.10230/) (2023)
- [Adaptive Control of SE(3) Hamiltonian Dynamics with Learned Disturbance Features](https://mlsanity.com/paper/2109.09974/) (2021)
- [Solving Continual Offline Reinforcement Learning with Decision Transformer](https://mlsanity.com/paper/2401.08478/) (2024)
- [Online Optimization with Feedback Delay and Nonlinear Switching Cost](https://mlsanity.com/paper/2111.00095/) (2021)
- [Decision Transformer as a Foundation Model for Partially Observable Continuous Control](https://mlsanity.com/paper/2404.02407/) (2024)
- [Continual Visual Reinforcement Learning with A Life-Long World Model](https://mlsanity.com/paper/2303.06572/) (2023)
- [Combining Federated Learning and Control: A Survey](https://mlsanity.com/paper/2407.11069/) (2024)
- [Meta-Learning Online Dynamics Model Adaptation in Off-Road Autonomous Driving](https://mlsanity.com/paper/2504.16923/) (2025)
- [Active Representation Learning for General Task Space with Applications in Robotics](https://mlsanity.com/paper/2306.08942/) (2023)
- [Meta-Learning-Based Adaptive Stability Certificates for Dynamical Systems](https://mlsanity.com/paper/2312.15340/) (2023)
- [Clustering-Based Weight Orthogonalization for Stabilizing Deep Reinforcement Learning](https://mlsanity.com/paper/2511.11607/) (2025)
- [Distributionally Safe Reinforcement Learning under Model Uncertainty: A Single-Level Approach by Differentiable Convex Programming](https://mlsanity.com/paper/2310.02459/) (2023)
- [Data-Guided Regulator for Adaptive Nonlinear Control](https://mlsanity.com/paper/2311.12230/) (2023)
- [Domain Invariant Learning for Gaussian Processes and Bayesian Exploration](https://mlsanity.com/paper/2312.11318/) (2023)
- [Model-Free versus Model-Based Reinforcement Learning for Fixed-Wing UAV Attitude Control Under Varying Wind Conditions](https://mlsanity.com/paper/2409.17896/) (2024)
- [T2S-MPC: Time-Embedded Online Adaptive Model Predictive Control for Time-Varying Dynamics](https://mlsanity.com/paper/2605.24852/) (2026)
- [Neural ODEs Meet Concurrent Learning: Stable Online Learning with Lyapunov Guarantees](https://mlsanity.com/paper/2609.32289/) (2026)

## Abstract (arXiv)

We present an online multi-task learning approach for adaptive nonlinear control, which we call Online Meta-Adaptive Control (OMAC). The goal is to control a nonlinear system subject to adversarial disturbance and unknown textitenvironment-dependent nonlinear dynamics, under the assumption that the environment-dependent dynamics can be well captured with some shared representation. Our approach is motivated by robot control, where a robotic system encounters a sequence of new environmental conditions that it must quickly adapt to. A key emphasis is to integrate online representation learning with established methods from control theory, in order to arrive at a unified framework that yields both control-theoretic and learning-theoretic guarantees. We provide instantiations of our approach under varying conditions, leading to the first non-asymptotic end-to-end convergence guarantee for multi-task nonlinear control. OMAC can also be integrated with deep representation learning. Experiments show that OMAC significantly outperforms conventional adaptive control approaches which do not learn the shared representation, in inverted pendulum and 6-DoF drone control tasks under varying wind conditions.