ZG trajectory generation of Van der Pol oscillator in affine-control form with division-by-zero problem handled

Zhang dynamics (ZD) and gradient dynamics (GD) are two types of powerful methods for online problems solving. In this paper, a classic nonlinear system of Van der Pol oscillator in the affine-control form is investigated. By combining the ZD and GD methods, a method called Zhang-gradient (ZG) method is proposed to design a ZG controller for the trajectory generation of the aforementioned nonlinear oscillator. Simulation results of ZG trajectory generation further demonstrate the feasibility and effectiveness of the ZG controller with the division-by-zero problem successfully handled. In addition, we investigate the effects of the ZD and GD design parameters on the ZG controller.