# Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems

arXiv: https://arxiv.org/abs/2103.04490 · HTML: https://mlsanity.com/paper/2103.04490/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 84 references that are in the map.
- First posted on arXiv 7 Mar 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)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [Meta-Learning with Differentiable Convex Optimization](https://mlsanity.com/paper/1904.03758/) (2019)
- [Meta-learning with differentiable closed-form solvers](https://mlsanity.com/paper/1805.08136/) (2018)
- [Learning to Adapt in Dynamic, Real-World Environments Through Meta-Reinforcement Learning](https://mlsanity.com/paper/1803.11347/) (2018)
- [Model-Ensemble Trust-Region Policy Optimization](https://mlsanity.com/paper/1802.10592/) (2018)
- [Differentiable MPC for End-to-end Planning and Control](https://mlsanity.com/paper/1810.13400/) (2018)
- [Neural Lyapunov Control](https://mlsanity.com/paper/2005.00611/) (2020)
- [EPOpt: Learning Robust Neural Network Policies Using Model Ensembles](https://mlsanity.com/paper/1610.01283/) (2016)
- [Model-Based Reinforcement Learning via Meta-Policy Optimization](https://mlsanity.com/paper/1809.05214/) (2018)
- [The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systems](https://mlsanity.com/paper/1808.00924/) (2018)
- [Adaptive Checkpoint Adjoint Method for Gradient Estimation in Neural ODE](https://mlsanity.com/paper/2006.02493/) (2020)
- [Learning Certified Control using Contraction Metric](https://mlsanity.com/paper/2011.12569/) (2020)
- [Meta-Learning Priors for Efficient Online Bayesian Regression](https://mlsanity.com/paper/1807.08912/) (2018)
- [Learning Stability Certificates from Data](https://mlsanity.com/paper/2008.05952/) (2020)
- [Stochastic Mirror Descent on Overparameterized Nonlinear Models: Convergence, Implicit Regularization, and Generalization](https://mlsanity.com/paper/1906.03830/) (2019)
- [Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Design](https://mlsanity.com/paper/1503.03144/) (2015)
- [Learning Stabilizable Nonlinear Dynamics with Contraction-Based Regularization](https://mlsanity.com/paper/1907.13122/) (2019)
- [Learning Convex Optimization Control Policies](https://mlsanity.com/paper/1912.09529/) (2019)
- [Model-Based Meta-Reinforcement Learning for Flight with Suspended Payloads](https://mlsanity.com/paper/2004.11345/) (2020)
- [Stochastic Gradient/Mirror Descent: Minimax Optimality and Implicit Regularization](https://mlsanity.com/paper/1806.00952/) (2018)
- [Beyond Convexity -- Contraction and Global Convergence of Gradient Descent](https://mlsanity.com/paper/1806.06655/) (2018)
- [Adaptive MPC for Iterative Tasks](https://mlsanity.com/paper/1804.09831/) (2018)
- [Deep Model Reference Adaptive Control](https://mlsanity.com/paper/1909.08602/) (2019)
- [Asynchronous Deep Model Reference Adaptive Control](https://mlsanity.com/paper/2011.02920/) (2020)
- [Linear Matrix Inequalities for Physically-Consistent Inertial Parameter Identification: A Statistical Perspective on the Mass Distribution](https://mlsanity.com/paper/1701.04395/) (2017)

## Built on by (most cited first, 30 of 39)

- [Neural-Fly Enables Rapid Learning for Agile Flight in Strong Winds](https://mlsanity.com/paper/2205.06908/) (2022)
- [Finetuning Offline World Models in the Real World](https://mlsanity.com/paper/2310.16029/) (2023)
- [A System-Level View on Out-of-Distribution Data in Robotics](https://mlsanity.com/paper/2212.14020/) (2022)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [ASID: Active Exploration for System Identification in Robotic Manipulation](https://mlsanity.com/paper/2404.12308/) (2024)
- [Meta-Adaptive Nonlinear Control: Theory and Algorithms](https://mlsanity.com/paper/2106.06098/) (2021)
- [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)
- [Control-oriented meta-learning](https://mlsanity.com/paper/2204.06716/) (2022)
- [Sample-Efficient Linear Representation Learning from Non-IID Non-Isotropic Data](https://mlsanity.com/paper/2308.04428/) (2023)
- [Meta-Learning of Neural State-Space Models Using Data From Similar Systems](https://mlsanity.com/paper/2211.07768/) (2022)
- [Adaptive Robust Model Predictive Control with Matched and Unmatched Uncertainty](https://mlsanity.com/paper/2104.08261/) (2021)
- [On the adaptation of in-context learners for system identification](https://mlsanity.com/paper/2312.04083/) (2023)
- [Adaptive Control of SE(3) Hamiltonian Dynamics with Learned Disturbance Features](https://mlsanity.com/paper/2109.09974/) (2021)
- [Data-Driven Control with Inherent Lyapunov Stability](https://mlsanity.com/paper/2303.03157/) (2023)
- [Meta-Learning for Physically-Constrained Neural System Identification](https://mlsanity.com/paper/2501.06167/) (2025)
- [Optimizing Closed-Loop Performance with Data from Similar Systems: A Bayesian Meta-Learning Approach](https://mlsanity.com/paper/2211.00077/) (2022)
- [Learning Control-Oriented Dynamical Structure from Data](https://mlsanity.com/paper/2302.02529/) (2023)
- [Safe Navigation in Unstructured Environments by Minimizing Uncertainty in Control and Perception](https://mlsanity.com/paper/2306.14601/) (2023)
- [Projected Neural Differential Equations for Learning Constrained Dynamics](https://mlsanity.com/paper/2410.23667/) (2024)
- [Online Algorithms and Policies Using Adaptive and Machine Learning Approaches](https://mlsanity.com/paper/2105.06577/) (2021)
- [Meta-SysId: A Meta-Learning Approach for Simultaneous Identification and Prediction](https://mlsanity.com/paper/2206.00694/) (2022)
- [Combining Federated Learning and Control: A Survey](https://mlsanity.com/paper/2407.11069/) (2024)
- [Adaptive Asynchronous Control Using Meta-learned Neural Ordinary Differential Equations](https://mlsanity.com/paper/2207.12062/) (2022)
- [Neural-Rendezvous: Provably Robust Guidance and Control to Encounter Interstellar Objects](https://mlsanity.com/paper/2208.04883/) (2022)
- [Graph Neural Network Expressivity and Meta-Learning for Molecular Property Regression](https://mlsanity.com/paper/2209.13410/) (2022)
- [Predictive Control and Regret Analysis of Non-Stationary MDP with Look-ahead Information](https://mlsanity.com/paper/2409.08434/) (2024)
- [Context-Aware Deep Lagrangian Networks for Model Predictive Control](https://mlsanity.com/paper/2506.15249/) (2025)
- [Adaptive Robust Model Predictive Control via Uncertainty Cancellation](https://mlsanity.com/paper/2212.01371/) (2022)
- [Model-Assisted Probabilistic Safe Adaptive Control With Meta-Bayesian Learning](https://mlsanity.com/paper/2307.00828/) (2023)

## Abstract (arXiv)

Real-time adaptation is imperative to the control of robots operating in complex, dynamic environments. Adaptive control laws can endow even nonlinear systems with good trajectory tracking performance, provided that any uncertain dynamics terms are linearly parameterizable with known nonlinear features. However, it is often difficult to specify such features a priori, such as for aerodynamic disturbances on rotorcraft or interaction forces between a manipulator arm and various objects. In this paper, we turn to data-driven modeling with neural networks to learn, offline from past data, an adaptive controller with an internal parametric model of these nonlinear features. Our key insight is that we can better prepare the controller for deployment with control-oriented meta-learning of features in closed-loop simulation, rather than regression-oriented meta-learning of features to fit input-output data. Specifically, we meta-learn the adaptive controller with closed-loop tracking simulation as the base-learner and the average tracking error as the meta-objective. With a nonlinear planar rotorcraft subject to wind, we demonstrate that our adaptive controller outperforms other controllers trained with regression-oriented meta-learning when deployed in closed-loop for trajectory tracking control.