ZG controllers for output tracking of nonlinear mass-spring-damper mechanical system with division-by-zero problem solved

Recently, two classes of dynamical methods, i.e., Zhang dynamics (ZD) and gradient dynamics (GD), have been widely investigated individually and comparatively for online time-varying problems solving. In this paper, by combining ZD and GD, an innovative method called Zhang-gradient (ZG) method is proposed for tracking control of a nonlinear mass-spring-damper (MSD) mechanical system. Simulation results substantiate the feasibility and effectiveness of the combined ZG method for handling both the explicit and implicit tracking-control problems. Especially, the z1g1 controller based on the ZG method for the implicit tracking control is also capable of conquering the division-by-zero problem.