Theory and Substantiation of z0g1 Controller Conquering Singularity Problem of Output Tracking for a Class of Nonlinear System

The conventional controller for output tracking of a class of nonlinear system is not valid when encountering the singularity (i.e., Division-by-zero) problem. To conquer the singularity problem, Zhang et al. Have proposed a simple yet effective controller design method, i.e., Aiding the conventional controller with gradient dynamics (GD), yielding a z0g1 controller in the framework of Zhang-gradient (ZG) method. As an in-depth research, this paper provides the theory and proof on the performance of this z0g1 controller, which is exploited to conquer the singularity problem while fulfilling the tracking-control task. Besides, simulations and experiments substantiate and complement the theoretical analyses of such a z0g1 controller.