Learning One-Step Inverse for Performance Improvement of Nonlinear Control Systems: Application to Quadrotor Control

초록

This paper proposes a learning-based control framework to enlarge the region of attraction of controllers for nonlinear systems subject to model uncertainties. When a nominal controller designed for an assumed nominal model is applied to a physical system, discrepancies between the model and the actual dynamics act as perturbations and degrade stability and performance. To mitigate this issue, we construct a controller that learns a one-step inverse of the dynamics via kernel methods. Unlike conventional methods that augment the nominal controller, the proposed approach does not rely on specific structural assumptions on the system dynamics and uncertainties. We provide a theoretical analysis guaranteeing that, under sufficient data-density conditions, the proposed controller yields smaller perturbations than those of the nominal controller in the closed-loop system. As a proof of concept, the effectiveness of the proposed method is experimentally validated on a micro-quadrotor. The results demonstrate an enlarged region of attraction compared to the nominal controller, even when using limited data (500 training input-output pairs) from a single episode.

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