An Approximation Method Using Simulation Data and Dynamical Model for Stable Manifolds in Forwarding Design

Abstract

This paper proposes a data-driven method to approximate stable manifolds in forwarding design. A control law designed with forwarding includes functions describing stable manifolds and their partial derivatives. In order to consider the approximation of partial derivatives, the proposed method constructs neural networks that fit the training data and also satisfy certain differential equations characterizing stable manifolds. We define a loss function suitable for this purpose based on the idea of Physics-Informed Neural Networks. A computational algorithm for learning with the proposed loss function is accordingly derived. The effectiveness of the proposed method is confirmed by application to an input-constrained nonlinear control for a planar quadrotor.