Output Tracking Control of Time-Varying Nonlinear Scalar Systems Using ZD and ZG Methods

Zhang dynamics (ZD) method and Zhang-gradient (ZG) method are widely used to solve time-invariant and time-varying problems. About the output tracking problem of time-varying nonlinear scalar (TVNS) systems, this paper attempts to design the controllers by using the ZD and ZG methods. Furthermore, the mathematical models of TVNS systems can be divided into three situations for analysis and discussion. To further measure the performances of the controllers, numerical experiments are conducted on some specific examples. Numerical results substantiate that the ZD and ZG methods are effective for TVNS systems, and that they have the ability to solve the division-by-zero problem in different manners. Besides, the output tracking errors of the controllers designed by using the ZD and ZG methods are nearly close to zero.