2025/10/03 by Tianhua Gao, Gao, Tianhua
Engineering · Physics and Astronomy · #Adaptive Control of Nonlinear Systems #Adaptive control #Artificial neural network #Control Systems and Identification #Control theory (sociology) #Convergence (economics) #Identification (biology) #Interpretability #Model Reduction and Neural Networks #Set (abstract data type) #Stability (learning theory) #System identification
paper · pdf · doi:10.48550/arxiv.2510.03100
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.