GD-aided IOL (input–output linearisation) controller for handling affine-form nonlinear system with loose condition on relative degree

ABSTRACT

Input–output linearisation (IOL) may encounter a singularity problem when applied to the tracking control of affine-form nonlinear system (AFNS), which may not have a well-defined relative degree. The singularity problem has occurred in the area of control for decades. In this paper, we incorporate the gradient dynamics (GD) into IOL, which leads to the GD-aided IOL method to solve the singularity problem, with the proposition of the loose condition on relative degree. Moreover, detailed theoretical analyses on tracking-error bound and convergence performance of the corresponding GD-aided IOL controller are presented. Simulations and comparisons substantiate that the proposed GD-aided IOL method is capable of completing the tracking-control task and conquering the singularity encountered in the AFNS.

Keywords:

• Input–output linearisation
• affine-form nonlinear system
• controller design
• loose condition on relative degree
• error bound

Acknowledgments

This work was supported by the National Natural Science Foundation of China (with number 61473323), by the Foundation of Key Laboratory of Autonomous Systems and Networked Control, Ministry of Education, China (with number 2013A07), and also by the Science and Technology Program of Guangzhou, China (with number 2014J4100057). The authors would like to thank the editors and anonymous reviewers sincerely for their time and effort spent in handling the paper, as well as many constructive comments provided for improving the presentation and quality of the paper very much.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61473323]; the Foundation of Key Laboratory of Autonomous Systems and Networked Control, Ministry of Education, China [grant number 2013A07]; the Science and Technology Program of Guangzhou, China [grant number 2014J4100057].