Finite-time containment control of perturbed multi-agent systems based on sliding-mode control

ABSTRACT

Aimed at faster convergence rate, this paper investigates finite-time containment control problem for second-order multi-agent systems with norm-bounded non-linear perturbation. When topology between the followers are strongly connected, the nonsingular fast terminal sliding-mode error is defined, corresponding discontinuous control protocol is designed and the appropriate value range of control parameter is obtained by applying finite-time stability analysis, so that the followers converge to and move along the desired trajectories within the convex hull formed by the leaders in finite time. Furthermore, on the basis of the sliding-mode error defined, the corresponding distributed continuous control protocols are investigated with fast exponential reaching law and double exponential reaching law, so as to make the followers move to the small neighbourhoods of their desired locations and keep within the dynamic convex hull formed by the leaders in finite time to achieve practical finite-time containment control. Meanwhile, we develop the faster control scheme according to comparison of the convergence rate of these two different reaching laws. Simulation examples are given to verify the correctness of theoretical results.

KEYWORDS:

• Multi-agent systems
• finite time
• practical containment control
• non-linear perturbation
• sliding-mode control

Acknowledgments

The authors would like to thank the editor-in-chief and the associate editor and the anonymous reviewers for their detailed comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This paper is partially supported by the National Natural Science Foundation of China [grant number 51404074], [grant number 61374127]; National Science Fund for Distinguished Young Scholars [grant number 61325003] and Projects of International Cooperation and Exchanges NSFC [grant number 61620106005].

Notes on contributors

Di Yu

Di Yu received the B.S. degree in industrial automation and the M.S. degree in control theory and control engineering from Northeast Petroleum University, Daqing, China, in 1998 and 2001, respectively, and the Ph.D. degree in control theory and engineering from Beijing Institute of Technology, Beijing, China, in 2013. She is currently an associate professor in the Department of Electronic Science, College of Smart City, Beijing Union University, Beijing, China. And she has published more than 20 referred conference and journal papers. Her current research interests include multi-agent coordination control, data mining and knowledge discovery, machine learning.

Xiang Yang Ji

Xiangyang Jireceived the B.S. degree in materials science and the M.S. degree in computer science from the Harbin Institute of Technology, Harbin, China, in 1999 and 2001, respectively, and the Ph.D. degree in computer science from the Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China. He joined Tsinghua University, Beijing, China, in 2008, where he is currently a Professor in the Department of Automation, School of Information Science and Technology. He has published more than 100 referred conference and journal papers. His current research interests include signal processing, image/video compression and communication, intelligent imaging.