Robust iterative learning protocols for finite-time consensus of multi-agent systems with interval uncertain topologies

Abstract

This paper is devoted to the robust finite-time output consensus problems of multi-agent systems under directed graphs, where all agents and their communication topologies are subject to interval uncertainties. Distributed protocols are constructed by using iterative learning control (ILC) algorithms, where information is exchanged only at the end of one iteration and learning is used to update the control inputs after each iteration. It is proved that under ILC-based protocols, the finite-time consensus can be achieved with an increasing number of iterations if the communication network of agents is guaranteed to have a spanning tree. Moreover, if the information of any desired terminal output is available to a portion (not necessarily all) of the agents, then the consensus output that all agents finally reach can be enabled to be the desired terminal output. It is also proved that for all ILC-based protocols, gain selections can be provided in terms of bound values, and consensus conditions can be developed associated with bound matrices. Simulation results are given to demonstrate the effectiveness of our theoretical results.

Keywords:

• iterative learning control
• multi-agent systems
• distributed protocol
• finite-time consensus
• robustness
• interval uncertainty

Acknowledgements

The authors thank the anonymous reviewers for their constructive comments and insightful suggestions which greatly improve the presentation of this paper. This work was supported by the National 973 Program (2012CB821200, 2012CB821201), the NSFC (61104011, 61134005, 61203022), the MOE (20111102120031), and the Beijing Natural Science Foundation (4122046).

Additional information

Notes on contributors

Deyuan Meng

Deyuan Meng received the BS degree in Mathematics and Applied Mathematics from Ocean University of China (OUC), Qingdao, China, in June 2005, and the PhD degree in Control Theory and Control Engineering from Beihang University (BUAA), Beijing, China, in July 2010. He is currently with the Seventh Research Division and the Department of Systems and Control at Beihang University. His research interests include iterative learning control and distributed control of multi-agent systems.

Yingmin Jia

Yingmin Jia received the BS degree in control theory from Shandong University, Ji'nan, China, in January 1982, and the MS and PhD degrees both in control theory and applications from Beihang University (BUAA), Beijing, China, in 1990 and 1993, respectively. In 1993, he joined the Seventh Research Division at Beihang University, where he is currently Professor of automatic control. From February 1995 until February 1996, he was a visiting professor with the Institute of Robotics and Mechatronics of the German Aerospace Center (DLR), Oberpfaffenhofen, Germany. He held an Alexander von Humboldt (AvH) research fellowship with the Institute of Control Engineering at the Technical University Hamburg-Harburg, Hamburg, Germany, from December 1996 until March 1998, and a JSPS research fellowship with the Department of Electrical and Electronic Systems at the Osaka Prefecture University, Osaka, Japan, from March 2000 until March 2002. He was a visiting professor with the Department of Statistics at the University of California Berkeley from December 2006 until March 2007. His current research interests include robust control, adaptive control and intelligent control, and their applications in industrial processes and vehicle systems. He is author and co-author of numerous papers and of the book ‘Robust H_∞ Control’ (Science Press, 2007).

Junping Du

Junping Du was born in Beijing, China. She received her PhD degree in computer science from University of Science and Technology Beijing (USTB), and then held a postdoc fellowship with the Department of Computer Science at Tsinghua University, Beijing, China. She joined the School of Computer Science at Beijing University of Posts and Telecommunications (BUPT) in July 2006, where she is currently Professor in computer science. She served as chair and co-chair of IPC for many international and domestic academic conferences, and has been vice general secretary of Chinese Association for Artificial Intelligence (CAAI) since 2004. She was a visiting professor with the Department of Computer Science at Aarhus University, Denmark, from September 1996 until September 1997. Her current research interests include artificial intelligence, data mining, intelligent management system development, and computer applications.