An Automatic Control Perspective on Parameterizing Generative Adversarial Network

This article presents a new perspective from control theory to interpret and solve the instability and mode collapse problems of generative adversarial networks (GANs). The dynamics of GANs are parameterized in the function space and control directed methods are applied to investigate GANs. First, the linear control theory is utilized to analyze and understand GANs. It is proved that the stability depends only on control parameters. Second, a proportional-integral-derivative (PID) controller is designed to improve its stability. GANs can be controlled to adaptively generate images by an overshoot rate that is only related to the PID control parameters. Third, a new PIDGAN is derived with a theoretical guarantee of stability. Fourth, to exploit the nonlinear characteristics of GANs, the nonlinear control theory is applied to further analyze GANs and develop a feedback linearization control-based PIDGAN named NPIDGAN. Both PIDGAN and NPIDGAN not only improve stability but also prevent mode collapse. With five datasets covering a wide variety of image domains, the proposed models achieve superior performance with 1024 $\times $ 1024 resolution compared with the state-of-the-art GANs, even when data are limited.