# MPC of Uncertain Nonlinear Systems with Meta-Learning for Fast Adaptation of Neural Predictive Models

arXiv: https://arxiv.org/abs/2404.12097 · HTML: https://mlsanity.com/paper/2404.12097/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 26 references that are in the map.
- First posted on arXiv 18 Apr 2024.

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

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [OpenAI Gym](https://mlsanity.com/paper/1606.01540/) (2016)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [Rapidly Adaptable Legged Robots via Evolutionary Meta-Learning](https://mlsanity.com/paper/2003.01239/) (2020)
- [Constructing Neural Network-Based Models for Simulating Dynamical Systems](https://mlsanity.com/paper/2111.01495/) (2021)
- [Fast Online Adaptation in Robotics through Meta-Learning Embeddings of Simulated Priors](https://mlsanity.com/paper/2003.04663/) (2020)
- [Meta-Learning Linear Quadratic Regulators: A Policy Gradient MAML Approach for Model-free LQR](https://mlsanity.com/paper/2401.14534/) (2024)
- [Comparing Transfer and Meta Learning Approaches on a Unified Few-Shot Classification Benchmark](https://mlsanity.com/paper/2104.02638/) (2021)
- [Identifying the Dynamics of a System by Leveraging Data from Similar Systems](https://mlsanity.com/paper/2204.05446/) (2022)
- [Meta-Learning of Neural State-Space Models Using Data From Similar Systems](https://mlsanity.com/paper/2211.07768/) (2022)
- [Optimizing Closed-Loop Performance with Data from Similar Systems: A Bayesian Meta-Learning Approach](https://mlsanity.com/paper/2211.00077/) (2022)
- [Data-based Transfer Stabilization in Linear Systems](https://mlsanity.com/paper/2211.05536/) (2022)

## Built on by (most cited first, 4 of 4)

- [Meta-Learning for Physically-Constrained Neural System Identification](https://mlsanity.com/paper/2501.06167/) (2025)
- [Manifold meta-learning for reduced-complexity neural system identification](https://mlsanity.com/paper/2504.11811/) (2025)
- [Meta-Learning for Rapid Adaptation in Reference Tracking of Uncertain Nonlinear Systems](https://mlsanity.com/paper/2605.22513/) (2026)
- [T2S-MPC: Time-Embedded Online Adaptive Model Predictive Control for Time-Varying Dynamics](https://mlsanity.com/paper/2605.24852/) (2026)

## Abstract (arXiv)

In this paper, we consider the problem of reference tracking in uncertain nonlinear systems. A neural State-Space Model (NSSM) is used to approximate the nonlinear system, where a deep encoder network learns the nonlinearity from data, and a state-space component captures the temporal relationship. This transforms the nonlinear system into a linear system in a latent space, enabling the application of model predictive control (MPC) to determine effective control actions. Our objective is to design the optimal controller using limited data from the textittarget system (the system of interest). To this end, we employ an implicit model-agnostic meta-learning (iMAML) framework that leverages information from textitsource systems (systems that share similarities with the target system) to expedite training in the target system and enhance its control performance. The framework consists of two phases: the (offine) meta-training phase learns a aggregated NSSM using data from source systems, and the (online) meta-inference phase quickly adapts this aggregated model to the target system using only a few data points and few online training iterations, based on local loss function gradients. The iMAML algorithm exploits the implicit function theorem to exactly compute the gradient during training, without relying on the entire optimization path. By focusing solely on the optimal solution, rather than the path, we can meta-train with less storage complexity and fewer approximations than other contemporary meta-learning algorithms. We demonstrate through numerical examples that our proposed method can yield accurate predictive models by adaptation, resulting in a downstream MPC that outperforms several baselines.