Paper Info
Title
Division by zero, pseudo-division by zero, Zhang dynamics method and Zhang-gradient method about control singularity conquering.
Abstract
In this paper, the division-by-zero DBO problem in the field of nonlinear control, which is traditionally termed the control singularity problem or specifically, controller singularity problem, is investigated by the Zhang dynamics ZD method and the Zhang-gradient ZG method. According to the impact of the DBO problem on the state variables of the controlled nonlinear system, the concepts of the pseudo-DBO problem and the true-DBO problem are proposed in this paper, which provide a new perspective for the researchers on the DBO problems as well as nonlinear control systems. Besides, the two classes of DBO problems are solved under the framework of the ZG method. Specific examples are shown and investigated in this paper to illustrate the two proposed concepts and the efficacy of the ZG method in conquering pseudo-DBO and true-DBO problems. The application of the ZG method to the tracking control of a two-wheeled mobile robot further substantiates the effectiveness of the ZG method. In addition, the ZG method is successfully applied to the tracking control of a pure-feedback nonlinear system.
Year
DOI
Venue
2017
10.1080/00207721.2016.1139761
Int. J. Systems Science
Keywords
Field
DocType
Division-by-zero problem, nonlinear control system, Zhang dynamics method, Zhang-gradient method
Division by zero,Gradient method,Control theory,Mathematical optimization,Nonlinear system,Control theory,Nonlinear control,Singularity,State variable,Mobile robot,Mathematics
Journal
Volume
Issue
ISSN
48
1
0020-7721
Citations 
PageRank 
References 
16
0.59
22
Authors
5
Name
Order
Citations
PageRank
Yunong Zhang12344162.43
Yinyan Zhang2672.43
Dechao Chen3192.01
Zhengli Xiao4433.17
xiaogang yan5373.74