Output consensus for multiple non-holonomic systems under directed communication topology

Abstract

In this paper, the problem of output consensus for multiple non-holonomic systems in chained form has been investigated. First, an output consensus controller under the strongly connected communication topology is devised by two steps, where a time-varying control strategy and the backstepping design technique are employed. Then, the results are extended to the general directed topology case via graph decomposition, in which the input-to-state stability theory plays a critical role. We prove that the proposed controller can achieve the semi-global output consensus among multiple non-holonomic systems, provided that the interaction graph contains a spanning tree. Finally, numerical examples are provided to illustrate the effectiveness of the designed controller.

Keywords:

• consensus
• backstepping
• non-holonomic system
• graph decomposition
• input-to-state stability (ISS)

Acknowledgements

This work was supported by the National Natural Science Foundation of China (under grants 60974041, 60934006 and 61273110), the Research Fund for the Doctoral Program of Higher Education of China (under grant 20090092110021) and the China Scholarship Council (CSC).

Additional information

Notes on contributors

Yaojin Xu

Yaojin Xu received his bachelor’s degree in Automation from Southeast University, Nanjing, China, in 2007. He is currently working towards his PhD degree in Control Theory and Control Engineering at the same university. His research interests include nonlinear control theory and cooperative control of multi-agent systems. Email: [email protected]

Yu-Ping Tian

Yu-Ping Tian received his bachelor’s degree from Tsinghua University, Beijing, China, in 1986, PhD degree from the Moscow Power Institute, Moscow, USSR, in 1991, and ScD degree from Taganrog State Radio-engineering University, Taganrog, Russia, in 1996. All his degrees are in Electrical Engineering. Since 1992, he has been with Southeast University, Nanjing, China, where he is a Professor with the School of Automation. He held visiting positions with Central Queensland University, Australia, University of California at Berkeley, and the City University of Hong Kong. He has published three books including Frequency-Domain Analysis and Design of Distributed Control Systems (John Wiley & Sons, 2012). His research interests are in the fields of control theory and networking. He is a recipient of the Chang Jiang Distinguished Professorship awarded by the Education Ministry of China and the Distinguished Young Scholar Award of the National Natural Science Foundation of China. Email: [email protected]

YangQuan Chen

YangQuan Chen earned his PhD degree in Advanced Control and Instrumentation from the Nanyang Technological University, Singapore, in 1998. Dr Chen was in the faculty of Electrical and Computer Engineering at Utah State University before he joined the School of Engineering, University of California, Merced, in 2012. His current research interests include mechatronics for sustainability, cognitive process control and hybrid lighting control, multi-unmanned aerial vehicle based cooperative multi-spectral ‘personal remote sensing’ and applications, applied fractional calculus in controls, signal processing and energy informatics, and distributed measurement and distributed control of distributed parameter systems using mobile actuator and sensor networks. He is a member of AMA, AWRA, AUVSI, ASME, IEEE and ASEE. He is an Associate Editor for Acta Montanistica Slovaca, Fractional Calculus and Applied Analysis (Springer), Fractional Differential Calculus, International Journal of Advanced Robotic Systems, ASME Journal of Dynamical Systems, Measurement and Control, IEEE Transactions of Control Systems Technology, ISA Transactions and the IFAC journals Journal of Mechatronics and Control Engineering Practice. He is also a founding editorial board member for Unmanned Systems (World Scientific), a senior editor for the Journal of Intelligent & Robotic Systems (Springer), and a member of the editorial board of An International Journal of Optimization and Control: Theories & Applications.