Extra ZD Aid to Output Tracking Control of Time-Varying Nonlinear Scalar Systems With Original Crash Solved

The problem of output tracking control for time-varying nonlinear scalar (TVNS) systems with the original crash is considered in this paper. Note that, due to the situation that control input is included in system output, the gradient dynamics (GD) method may be failed to design an effective controller. Therefore, an extra Zhang dynamics aid (extra-ZD-aid) method is proposed to solve the original crash of TVNS systems. Besides, the special TVNS systems are divided into four situations for discussion. The corresponding mathematical derivations and specific examples are also presented. Moreover, the numerical results substantiate that the controllers by utilizing the extra-ZD-aid method not only achieve satisfactory tracking control performance, but also successfully eliminate the original crash of TVNS systems.