Output Tracking of Time-Varying Linear and Nonlinear Systems Using ZN and ZG Controllers with Pseudo Division-by-Zero Phenomena Shown

This paper introduces Zhang neurodynamics (ZN) method and Zhang-gradient (ZG) method used to design ZN and ZG controllers for the output tracking of systems, especially time-varying nonlinear system. Thereinto, ZG method is composed of the ZN method and gradient neurodynamics (GN) method. By applying the ZN method and the ZG method, respectively, to the output tracking control problems of time-varying linear (TVL) system and time-varying nonlinear (TVN) system, specific ZN controllers and ZG controllers are obtained. Particularly, TVL system and TVN system discussed in this paper may both have pseudo division-by-zero phenomena. From the numerical results, though ZN controllers and ZG controllers perform the output tracking of TVL system and TVN system well, the infinite value of the former and the finite value of the latter at singular instants verify that the ZG method is more effective in dealing with pseudo division-by-zero problem.