Abstract
This brief paper studies the consensus problem of second-order multi-agent systems when the agents’ velocity measurements are unavailable. Firstly, two simple consensus protocols which do not need velocity measurements of the agents are derived to guarantee that the multi-agent systems achieve consensus in directed networks. Secondly, a key constant which is determined by the complex eigenvalue of the nonsymmetric Laplacian matrix and an explicit expression of the consensus state are respectively developed based on matrix theory. The obtained results show that all the agents can reach consensus if the feedback parameter is bigger than the key constant. Thirdly, the theoretical analysis shows that the followers can track the position and velocity of the leader provided that the leader has a directed path to all other followers and the feedback parameter is bigger enough. Finally, numerical simulations are given to illustrate the effectiveness of the proposed protocols.
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Recommended by Associate Editor Augie Widyotriatmo under the direction of Editor Myo Taeg Lim. This work was supported by the National Science Foundation of China (Grant No. 61673351), the Postdoctoral Science Foundation of Zhejiang Province (Grant No. Z42103001).
Shan Cheng received his Ph.D. degree in Shanghai University in 2012. His research interests include consensus of multi-agent systems, control of nonlinear systems and robotics, control of networks of dynamical systems, etc.
Han Dong received his B.S. degree in Lvliang College in 2016. He is currently working toward a M.S. degree Zhejiang University of Technology. His research interests include consensus of multi-agent systems, control of nonlinear systems, etc.
Li Yu received the B.S. degree in Control Theory from Nankai University in 1982, and the M.S. and Ph.D. degrees from Zhejiang University, Hangzhou, China. He is currently a Professor in the Department of Automation, Zhejiang University of Technology, P. R. China. He has authored or co-authored 5 books and over 400 journal or conference papers. His current research interests include networked control systems, information fusion, motion control, etc.
Dongmei Zhang received the Ph.D. degree in Control Theory and Application at Zhejiang University of Technology. Her early work focuses on the stability of general linear time-delay systems. Her latest work focuses on the networked multiagent system control, estimation and filtering theory, information fusion estimation, etc.
Jinchen Ji received his B.S., M.S. and Ph.D. degrees all in Mechanical Engineering (dynamics and control). He is currently an Associate Professor in Mechanical and Mechatronic Engineering at the University of Technology Sydney (UTS). His research interests include dynamics and control of mechanical systems, synchronization and consensus of networked multi-agent systems, control of nonlinear mechanical systems, dynamics of time-delayed nonlinear systems, control of flexible manipulator, vehicle system dynamics, and wind turbine dynamics.
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Cheng, S., Dong, H., Yu, L. et al. Consensus of Second-order Multi-agent Systems with Directed Networks Using Relative Position Measurements Only. Int. J. Control Autom. Syst. 17, 85–93 (2019). https://doi.org/10.1007/s12555-018-0148-0
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DOI: https://doi.org/10.1007/s12555-018-0148-0