Quasi-finite-time control for high-order nonlinear systems with mismatched disturbances via mapping filtered forwarding technique

ABSTRACT

In this study, a quasi-finite-time control method for designing stabilising control laws is developed for high-order strict-feedback nonlinear systems with mismatched disturbances. By using mapping filtered forwarding technique, a virtual control is designed to force the off-the-manifold coordinate to converge to zero in quasi-finite time at each step of the design; at the same time, the manifold is rendered insensitive to time-varying, bounded and unknown disturbances. In terms of standard forwarding methodology, the algorithm proposed here not only does not require the Lyapunov function for controller design, but also avoids to calculate the derivative of sign function. As far as the dynamic performance of closed-loop systems is concerned, we essentially obtain the finite-time performances, which is typically reflected in the following aspects: fast and accurate responses, high tracking precision, and robust disturbance rejection. Spring, mass, and damper system and flexible joints robot are tested to demonstrate the proposed controller performance.

KEYWORDS:

• High-order nonlinear systems
• mapping filtered forwarding technique
• quasi-finite-time control
• disturbance rejection
• dynamic performance

Acknowlegdments

The authors are grateful to the Editor-in-Chief, the Associate Editor, the Production Editor, and anonymous reviewers for their valuable comments, based on which the presentation of this paper has been greatly improved.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Notethat the superscript [ · ] denotes the order of the target system.

2. Notethat when i = 1, the coordinate ${\tilde{\zeta }}^{\left[0\right]}$ denotes x^[1]₁, i.e. ${\tilde{\zeta }}^{\left[0\right]}=x_1^{\left[1\right]}$.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 51275107], [grant number 61304006], [grant number 61273095]; and the Innovative Team Program of the National Natural Science Foundation of China [grant number 61021002].

Notes on contributors

X. Zhang

Xu Zhang was born in 1986. He received his M.S. degree from Harbin Institute of Technology in 2010. Currently, he is a Ph.D. candidate at the Center for Control Theory and Guidance Technology, Harbin Institute of Technology. His current research interests include control of underactuated mechanical systems, robust and adaptive nonlinear control, immersion and invariance control.

X. L. Huang

Xianlin Huang was born in 1956. He received his M.S. and Ph.D. degrees from Harbin Institute of Technology in 1985 and 1991, respectively. He is now a professor in the Department of Control Science and Control Engineering, Harbin Institute of Technology. His research interests include robust and adaptive control, complex system control, navigation and control techniques in aerospace engineering.

H. Q. Lu

Hongqian Lu was born in 1975. He received his M.S. and Ph.D. degrees from Harbin Institute of Technology in 2000 and 2006, respectively. Now he is an associate professor in the Department of Control Science and Control Engineering, Harbin Institute of Technology. His research interests include nonlinear control and applications, intelligent navigation and control techniques.