Physics-Informed Learning of Feedback-Linearizing Representations
Feedback linearization is a powerful tool in nonlinear control, but finding the linearizing coordinate transform remains challenging. Feedback linearizing transforms are governed by well-established partial differential equations (PDEs) whose well-posedness is based on the Lie-algebraic Frobenius theorem, but solving the PDEs becomes computationally intractable for large system dimensions. To address this challenge, we propose a cascaded physics-informed neural network (PINN) framework to approximately solve these PDEs. By separately parameterizing terms of different Lie derivative orders, we mitigate the compounding errors inherent in fitting high-order Lie derivatives of neural networks. Furthermore, we use the learned transform to design a tracking controller and establish theoretical bounds on its error with respect to inaccuracies in the learned feedback-linearizing representation. We validate our method on a broad class of feedback linearizable systems, including a multi-input, multi-output planar quadrotor and synthetic examples for which analytical approaches are impractical, and demonstrate that our approach can computationally discover effective feedback-linearizing representations of nonlinear systems for control tasks.