通过分维学习提升四旋翼在复杂扰动下的在线识别能力
A Dimension-Decomposed Learning Framework for Online Disturbance Identification in Quadrotor SE(3) Control
- 将高维映射分解为多个低维子任务，用浅层神经网络和自适应律分别处理
- 无需预训练或持续激励条件，实现对时变扰动的在线稳定识别
- 理论证明系统具任意接近指数稳定的闭环性能，适合实际飞行控制
四旋翼在复杂动态扰动和模型不确定性下的稳定性面临严峻挑战，现有基于学习的方法受限于高维特征的欠拟合问题。为此，本文提出维度分解学习（DiD-L）新视角，构建切片自适应神经映射（SANM）方法用于几何控制。将高维识别映射沿轴向分解为多个低维子映射（切片），将复杂高维问题转化为一系列由浅层神经网络与自适应律解决的简单低维任务。这些网络与自适应律通过李雅普诺夫方法在线更新，无需预训练或持续激励（PE）条件。为增强可解释性，理论证明全状态闭环系统在多维时变扰动与模型不确定性下仍具任意接近指数稳定性。该结果新颖地展示了无需预训练未知扰动或模型先验知识即可实现指数收敛。
原文摘要 · Abstract (English)
Quadrotor stability under complex dynamic disturbances and model uncertainties poses significant challenges. One of them remains the underfitting problem in high-dimensional features, which limits the identification capability of current learning-based methods. To address this, we introduce a new perspective: Dimension-Decomposed Learning (DiD-L), from which we develop the Sliced Adaptive-Neuro Mapping (SANM) approach for geometric control. Specifically, the high-dimensional mapping for identification is axially ``sliced" into multiple low-dimensional submappings (``slices"). In this way, the complex high-dimensional problem is decomposed into a set of simple low-dimensional tasks addressed by shallow neural networks and adaptive laws. These neural networks and adaptive laws are updated online via Lyapunov-based adaptation without any pre-training or persistent excitation (PE) condition. To enhance the interpretability of the proposed approach, we prove that the full-state closed-loop system exhibits arbitrarily close to exponential stability despite multi-dimensional time-varying disturbances and model uncertainties. This result is novel as it demonstrates exponential convergence without requiring pre-training for unknown disturbances and specific knowledge of the model.
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