Recovering Robust Feedback Linearization with Generative Adversarial Networks for Uncertain High-Order Nonlinear Systems: A Path to Safe Learning and Practical Deployment

This article proposes a data-driven methodology that employs generative adversarial networks (GANs) to approximate an exact feedback linearization (FL) controller, regulating a suite of high-order, uncertain, nonlinear systems. Considering the constraints of accessible training data, the estimation of system uncertainty is achieved through adversarial training between the generator and the discriminator. Subsequently, the deployment of the well-trained generator as a compensator fosters the formation of a linear relationship between the system's input and output. A comprehensive theoretical analysis is presented, demonstrating the guaranteed convergence in the safe recovery of a robust FL controller. Notably, the mode collapse issue, which is typically problematic in GANs training, is resolved by the strict convexity of the synthesized objective loss and the globally stable dynamics inherent in the designed GANs. Beyond numerical verification, we leverage a real-world servo mechanism experimental platform to demonstrate the efficacy of our proposed algorithm.