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This paper considers the output tracking control of general-form single-input single-output (SISO) nonlinear system, which may encounter the problem of division by zero (DBZ). First, via the Zhang dynamics (ZD) method, a ZD controller is proposed. Then, based on the ZD controller with the aid of gradient dynamics (GD) method, a Zhang-gradient (ZG) controller is proposed. For comparison, the conventional input-output linearization (IOL) controller is presented. The ZD, ZG and IOL controllers are compared in different relative-degree cases ( i.e., the standard relative-degree case, the loose relative-degree case and the DBZ relative-degree case). Note that the ZG controller is valid in three relative-degree cases, while the ZD and IOL controllers are valid only in the standard relative-degree case and the loose relative-degree case. In addition, performances of ZD and ZG controllers are guaranteed via theoretical analyses and computer simulations for the output tracking of general-form nonlinear system with the DBZ problem conquered. [ABSTRACT FROM AUTHOR]

This study investigates the tracking‐control problems of the Lorenz, Chen and Lu chaotic systems. Note that the input–output linearisation method cannot solve these tracking‐control problems because of the existence of singularities, at which such chaotic systems fail to have a well‐defined relative degree. By combining Zhang dynamics and gradient dynamics, an effective controller‐design method, termed Zhang‐gradient (ZG) method, is proposed for tracking control of the three chaotic systems. This ZG method, with singularities conquered, is capable of solving the tracking‐control problems of the chaotic systems. Both theoretical analyses and simulative verifications substantiate that the tracking controllers based on the ZG method can achieve satisfactory tracking accuracy and successfully conquer singularities encountered during the tracking‐control process. [ABSTRACT FROM AUTHOR]