# Meta-Learning for Rapid Adaptation in Reference Tracking of Uncertain Nonlinear Systems

arXiv: https://arxiv.org/abs/2605.22513 · HTML: https://mlsanity.com/paper/2605.22513/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 35 references that are in the map.
- First posted on arXiv 21 May 2026.

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

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [Bayesian Meta-Learning for Few-Shot Policy Adaptation Across Robotic Platforms](https://mlsanity.com/paper/2103.03697/) (2021)
- [Meta-Learning Linear Quadratic Regulators: A Policy Gradient MAML Approach for Model-free LQR](https://mlsanity.com/paper/2401.14534/) (2024)
- [Meta-Learning of Neural State-Space Models Using Data From Similar Systems](https://mlsanity.com/paper/2211.07768/) (2022)
- [Bridging direct & indirect data-driven control formulations via regularizations and relaxations](https://mlsanity.com/paper/2101.01273/) (2021)
- [Meta-Learning for Physically-Constrained Neural System Identification](https://mlsanity.com/paper/2501.06167/) (2025)
- [Meta-Learning with Adjoint Methods](https://mlsanity.com/paper/2110.08432/) (2021)
- [System Identification via Meta-Learning in Linear Time-Varying Environments](https://mlsanity.com/paper/2010.14664/) (2020)
- [MPC of Uncertain Nonlinear Systems with Meta-Learning for Fast Adaptation of Neural Predictive Models](https://mlsanity.com/paper/2404.12097/) (2024)

## Abstract (arXiv)

In this paper, we address the problem of reference tracking for uncertain nonlinear systems. Since collecting data from the target system (i.e., the system of interest) is often challenging, our objective is to design optimal controllers using limited target system data. Meta-learning provides a promising paradigm by leveraging offline data from source systems (systems sharing structural similarities with the target system) to accelerate training and enhance control performance. Motivated by this idea, we propose a meta-learning-based control framework that tailors the implicit model-agnostic meta-learning (iMAML) algorithm to the control setting. The framework operates in two phases: an (offline) meta-training phase, where an aggregated representation is learned from source data to capture the shared system dynamics among similar systems, and an (online) meta-adaptation phase, where this representation is fine-tuned on the target system using only a few data samples and limited adaptation steps. We formulate this framework as a bi-level optimization problem and provide an efficient solution with reduced storage complexity and few approximations. The proposed framework is general, allowing various learning algorithms to be integrated. To demonstrate this flexibility, we propose two specific learning algorithms that can be incorporated into our framework based on a neural state-space model and a deep Q-network, respectively. The primary distinction between these approaches is whether explicit system identification is required. Numerical simulations and hardware experiments demonstrate that the proposed methods enhance control performance and consistently outperform baseline approaches.