Formation tracking control for multi-agent systems: A wave-equation based approach


This paper considers the formation tracking control problem of large-scaled Multi-Agent Systems (MAS) for which the model is based on a system of mutually independent wave Partial Differential Equations (PDEs). The spatial derivatives in the equation correspond to the underlying communication topology of the agents. A leader-follower mode is employed in the control algorithm, with which the agents on the boundary of PDEs are chosen as leaders knowing the tracking trajectory and all the other agents are followers. Each follower has only the information of its own relative position and velocity to its topological neighbors. With a designed distributed controller, the formation tracking error is bounded by a constant proportional to the acceleration of the desired trajectory. Robustness of the control law to a perturbation in the velocity measurement is also discussed. Furthermore, some simulation studies are provided to show the effectiveness of the control algorithm.

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Corresponding author

Correspondence to Jie Qi.

Additional information

Recommended by Associate Editor Hyo-Sung Ahn under the direction of Editor Duk-Sun Shim. This work was partially supported by National Natural Science Foundation of China 61773112, 61473265, Natural Science Foundation of Shanghai 16ZR1401200 and the Fundamental Research Funds for the Central Universities 2232015D3-24.

Shu-Xia Tang received her Ph.D. in Mechanical Engineering in 2016 from the Department of Mechanical & Aerospace Engineering, University of California, San Diego, USA. She is currently a postdoctoral research fellow and lecturer at the Department of Applied Mathematics, University of Waterloo, Canada. Her main research interests are control and estimation in distributed parameter systems. Recent research also includes optimal actuator and sensor design problems.

Jie Qi received the Ph.D. degree in Systems Engineering (2005) and the B.S. degree in Automation (2000) from Northeastern University in Shenyang, China. She is currently a Professor in Automation Department, Donghua University, China. Her research interests include multi-agent cooperative control, the control of distributed parameter systems, complex system modeling and intelligent optimization.

Jing Zhang is currently pursuing the Ph.D. degree with the College of Information Science and Technology, Donghua University, Shanghai, China. She received the M.S. degree in Control Science and Engineering (2017) from Donghua University and the B.S. degree in Automation (2013) from Shanxi University, Taiyuan, China. Her research interests include boundary control and multi-agent cooperative control.

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Tang, SX., Qi, J. & Zhang, J. Formation tracking control for multi-agent systems: A wave-equation based approach. Int. J. Control Autom. Syst. 15, 2704–2713 (2017).

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  • Distributed control
  • formation tracking
  • MAS
  • robustness
  • wave PDE