Continual Uncertainty Learning for Robust Control of Nonlinear Systems with Multiple Heterogeneous Uncertainties

Learning-based control methods typically assume stationary system dynamics, an assumption often violated in real-world systems due to drift, wear, or changing operating conditions. We study reinforcement learning for control under time-varying dynamics. We consider a continual model-based reinforcement learning setting in which an agent repeatedly learns and controls a dynamical system whose transition dynamics evolve across episodes. We analyze the problem using Gaussian process dynamics models under frequentist variation-budget assumptions. Our analysis shows that persistent non-stationarity requires explicitly limiting the influence of outdated data to maintain calibrated uncertainty and meaningful dynamic regret guarantees. Motivated by these insights, we propose a practical optimistic model-based reinforcement learning algorithm with adaptive data buffer mechanisms and demonstrate improved performance on continuous control benchmarks with non-stationary dynamics.

Koopman operator theory provides a powerful framework for representing nonlinear dynamics through a linear operator acting on lifted observables, enabling the use of linear control techniques for nonlinear systems. However, Koopman models are typically learned from data and often degrade in performance under model uncertainty and distributional shifts between training and deployment. Although several works have explored online adaptation to address this issue, many rely on neural network-based updates that introduce significant computational overhead and lack formal safety guarantees, limiting their suitability for real-time and safety-critical robotic applications. In this work, we propose a unified framework for continual adaptive Koopman learning that enables safe and efficient online refinement of learned models during task execution. An autoencoder-based Koopman model is first learned offline and subsequently refined online through a contractive adaptation law, which provides theoretical convergence guarantees under distributional shifts and model uncertainty. To improve data efficiency and accelerate model refinement, the adaptation mechanism is integrated with an active learning strategy that drives the system to collect informative data while accomplishing task objectives. The resulting control problem is formulated as a nonconvex optimization problem incorporating both active learning objectives and safety constraints. We further derive theoretical bounds on model approximation error and show how these bounds can be incorporated within a robust Model Predictive Control (MPC) framework to provide formal safety guarantees. The proposed approach unifies learning, excitation, and safety within a single control framework without sacrificing real-time feasibility. Extensive simulation and experimental studies demonstrate superior performance compared to state-of-the-art baselines.

Learning-based Lyapunov Control (LLC) provides formal stability guarantees for nonlinear systems, but its validity relies heavily on accurate system models. Parameter variations and uncertainties may invalidate stability constraints, leading to costly retraining. Although D-learning can estimate Lyapunov derivatives without relying on explicit dynamics models, it remains limited by single-task dynamics and degrades under large parameter shifts. We propose Reptile-D-learning, a framework that leverages the Reptile meta-learning algorithm to capture shared dynamical structures across systems with different parameters, thereby learning a generalizable Lyapunov network initialization and a high-performance controller. Experiments on multiple nonlinear control systems demonstrate that Reptile-D-learning significantly improves both generalization and rapid adaptation to unseen parameter configurations.