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

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