This letter proposes an anti-disturbance control scheme for rotor drones to counteract voltage drop (VD) disturbance caused by voltage drop of the battery, which is a common case for long-time flight or aggressive maneuvers. Firstly, the refined dynamics of rotor drones considering VD disturbance are presented. Based on the dynamics, a voltage drop observer (VDO) is developed to accurately estimate the VD disturbance by decoupling the disturbance and state information of the drone, reducing the conservativeness of conventional disturbance observers. Subsequently, the control scheme integrates the VDO within the translational loop and a fixed-time sliding mode observer (SMO) within the rotational loop, enabling it to address force and torque disturbances caused by voltage drop of the battery. Sufficient real flight experiments are conducted to demonstrate the effectiveness of the proposed control scheme under VD disturbance.

The well-known generalization problem hinders the application of artificial neural networks in continuous-time prediction tasks with varying latent dynamics. In sharp contrast, biological systems can neatly adapt to evolving environments benefiting from real-time feedback mechanisms. Inspired by the feedback philosophy, we present feedback neural networks, showing that a feedback loop can flexibly correct the learned latent dynamics of neural ordinary differential equations (neural ODEs), leading to a prominent generalization improvement. The feedback neural network is a novel two-DOF neural network, which possesses robust performance in unseen scenarios with no loss of accuracy performance on previous tasks. A linear feedback form is presented to correct the learned latent dynamics firstly, with a convergence guarantee. Then, domain randomization is utilized to learn a nonlinear neural feedback form. Stemming from residual neural networks (He et al., 2016), neural ordinary differential equation (neural ODE) (Chen et al., 2018) emerges as a novel learning strategy aiming at learning the latent dynamic model of an unknown system. Recently, neural ODEs have been successfully applied to various scenarios, especially continuous-time missions (Liu & Stacey, 2024; Verma et al., 2024; Greydanus et al., 2019; Cranmer et al., 2020). However, like traditional neural networks, the generalization problem limits the application of neural ODEs in real-world applications. Traditional strategies like model simplification, fit coarsening, data augmentation, and transfer learning have considerably improved the generalization performance of neural networks on unseen tasks (Rohlfs, 2022). However, these strategies usually reduce the Figure 1: Neural network architectures.

High-precision control for nonlinear systems is impeded by the low-fidelity dynamical model and external disturbance. Especially, the intricate coupling between internal uncertainty and external disturbance is usually difficult to be modeled explicitly. Here we show an effective and convergent algorithm enabling accurate estimation of the coupled disturbance via combining control and learning philosophies. Specifically, by resorting to Chebyshev series expansion, the coupled disturbance is firstly decomposed into an unknown parameter matrix and two known structures depending on system state and external disturbance respectively. A Regularized Least Squares (RLS) algorithm is subsequently formalized to learn the parameter matrix by using historical time-series data. Finally, a higher-order disturbance observer (HODO) is developed to achieve a high-precision estimation of the coupled disturbance by utilizing the learned portion. The efficiency of the proposed algorithm is evaluated through extensive simulations. We believe this work can offer a new option to merge learning schemes into the control framework for addressing existing intractable control problems.