# T2S-MPC: Time-Embedded Online Adaptive Model Predictive Control for Time-Varying Dynamics

arXiv: https://arxiv.org/abs/2605.24852 · HTML: https://mlsanity.com/paper/2605.24852/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 48 references that are in the map.
- First posted on arXiv 24 May 2026.

## Builds on (most cited first, 23 of 23)

- [Understanding deep learning requires rethinking generalization](https://mlsanity.com/paper/1611.03530/) (2016)
- [Neural-Fly Enables Rapid Learning for Agile Flight in Strong Winds](https://mlsanity.com/paper/2205.06908/) (2022)
- [safe-control-gym: a Unified Benchmark Suite for Safe Learning-based Control and Reinforcement Learning in Robotics](https://mlsanity.com/paper/2109.06325/) (2021)
- [Real-time Neural-MPC: Deep Learning Model Predictive Control for Quadrotors and Agile Robotic Platforms](https://mlsanity.com/paper/2203.07747/) (2022)
- [Adaptive-Control-Oriented Meta-Learning for Nonlinear Systems](https://mlsanity.com/paper/2103.04490/) (2021)
- [Adaptive Regret for Control of Time-Varying Dynamics](https://mlsanity.com/paper/2007.04393/) (2020)
- [KNODE-MPC: A Knowledge-based Data-driven Predictive Control Framework for Aerial Robots](https://mlsanity.com/paper/2109.04821/) (2021)
- [Meta-Adaptive Nonlinear Control: Theory and Algorithms](https://mlsanity.com/paper/2106.06098/) (2021)
- [Performance, Precision, and Payloads: Adaptive Nonlinear MPC for Quadrotors](https://mlsanity.com/paper/2109.04210/) (2021)
- [Online Dynamics Learning for Predictive Control with an Application to Aerial Robots](https://mlsanity.com/paper/2207.09344/) (2022)
- [Learning for CasADi: Data-driven Models in Numerical Optimization](https://mlsanity.com/paper/2312.05873/) (2023)
- [Online Control of Unknown Time-Varying Dynamical Systems](https://mlsanity.com/paper/2202.07890/) (2022)
- [Meta-Learning of Neural State-Space Models Using Data From Similar Systems](https://mlsanity.com/paper/2211.07768/) (2022)
- [Meta-Learning Online Control for Linear Dynamical Systems](https://mlsanity.com/paper/2208.10259/) (2022)
- [Locally Weighted Regression Pseudo-Rehearsal for Online Learning of Vehicle Dynamics](https://mlsanity.com/paper/1905.05162/) (2019)
- [MPC of Uncertain Nonlinear Systems with Meta-Learning for Fast Adaptation of Neural Predictive Models](https://mlsanity.com/paper/2404.12097/) (2024)
- [Online Simultaneous Semi-Parametric Dynamics Model Learning](https://mlsanity.com/paper/1910.04297/) (2019)
- [Adaptive Control of Time-Varying Parameter Systems with Asymptotic Tracking](https://mlsanity.com/paper/2007.11801/) (2020)
- [I-DREM MRAC with Time-Varying Adaptation Rate & No A Priori Knowledge of Control Input Matrix Sign to Relax PE Condition](https://mlsanity.com/paper/2102.10785/) (2021)
- [Composite Adaptive Control for Time-varying Systems with Dual Adaptation](https://mlsanity.com/paper/2206.01700/) (2022)
- [A Tutorial on Gaussian Process Learning-based Model Predictive Control](https://mlsanity.com/paper/2404.03689/) (2024)
- [Learning a Terrain- and Robot-Aware Dynamics Model for Autonomous Mobile Robot Navigation](https://mlsanity.com/paper/2409.11452/) (2024)
- [Fast Online Adaptive Neural MPC via Meta-Learning](https://mlsanity.com/paper/2504.16369/) (2025)

## Abstract (arXiv)

Recent advances in learning-based model predictive control (MPC) have leveraged neural networks for online model learning, achieving strong performance when nonstationary system dynamics deviate from nominal models. However, existing approaches primarily address specific or relatively structured forms of dynamical variation, leaving more general, unknown, and unpredictable time-varying dynamics insufficiently handled. To tackle this challenge, we propose T2S-MPC, a framework that adaptively learns a residual dynamics model online and integrates it with the nominal model within the MPC framework to enable fast-evolving online planning. To make the model time-aware, we explicitly encode temporal information through a structured time embedding and employ a two-timescale update scheme, allowing the controller to capture nonstationary dynamics while balancing rapid adaptation with stable learning. We evaluate the proposed method on a 2D quadrotor across stabilization and trajectory tracking tasks under diverse time-varying disturbances, including linear drifting and periodic perturbations. Experimental results show that T2S-MPC consistently outperforms classical MPC, neural MPC, and ablated variants in control performance, while also demonstrating strong robustness across a wide range of disturbance conditions without additional tuning. The source code is publicly available at https://github.com/Zeyuu0920/T2S_MPC