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Distributed optimal consensus of multiple double integrators under bounded velocity and acceleration

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Abstract

This paper studies a distributed optimal consensus problem for multiple double integrators under bounded velocity and acceleration. Assigned with an individual and private convex cost which is dependent on the position, each agent needs to achieve consensus at the optimum of the aggregate cost under bounded velocity and acceleration. Based on relative positions and velocities to neighbor agents, we design a distributed control law by including the integration feedback of position and velocity errors. By employing quadratic Lyapunov functions, we solve the optimal consensus problem of double-integrators when the fixed topology is strongly connected and weight-balanced. Furthermore, if an initial estimate of the optimum can be known, then control gains can be properly selected to achieve an exponentially fast convergence under bounded velocity and acceleration. The result still holds when the relative velocity is not available, and we also discuss an extension for heterogeneous Euler-Lagrange systems by inverse dynamics control. A numeric example is provided to illustrate the result.

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Authors and Affiliations

  1. School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, 639798, Singapore

    Zhirong Qiu & Lihua Xie

  2. Key Laboratory of Systems and Control, Institute of Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Yiguang Hong

Authors
  1. Zhirong Qiu
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  2. Lihua Xie
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  3. Yiguang Hong
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Corresponding author

Correspondence to Lihua Xie.

Additional information

Zhirong Qiu received the B.Sc. and M.Sc. degrees in Applied Mathematics both from Sun Yat-Sen University, Guangzhou, China, and the Ph.D. degree from Nanyang Technological University (NTU), Singapore, in 2017. He is currently working as Research Fellow in the NTU-Delta Corporate Lab for Cyber-Physical Systems. His research interests include multi-agent systems and distributed optimization.

Lihua XIE received the B.E. and M.E. degrees in Electrical Engineering from Nanjing University of Science and Technology in 1983 and 1986, respectively, and the Ph.D. degree in Electrical Engineering from the University of Newcastle, Australia, in 1992. Since 1992, he has been with the School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore, where he is currently a professor and Director, Delta-NTU Corporate Laboratory for Cyber-Physical Systems. He served as the Head of Division of Control and Instrumentation from July 2011 to June 2014. Dr Xie’s research interests include robust control and estimation, networked control systems, multi-agent networks, and unmanned systems. He is currently an Editor-in-Chief of Unmanned Systems and has served as an editor of IET Book Series in Control and an Associate Editor of a number of journals including IEEE Transactions on Automatic Control, Automatica, IEEE Transactions on Control Systems Technology, IEEE Transactions on Control of Network Systems, and IEEE Transactions on Circuits and Systems-II, etc. Dr Xie is a Fellow of IEEE, Fellow of IFAC, and a member of Board of Governors, IEEE Control System Society.

Yiguang HONG received his B.Sc. and M.Sc. both from Peking University, and his Ph.D. degree from Institute of Systems Science, Chinese Academy of Sciences (CAS). He is a Guan Zhaozhi Chair Professor of Academy of Mathematics and Systems Science, CAS. His current research interests include nonlinear control, multi-agent networks, distributed optimization and game, machine learning, and social networks.

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Qiu, Z., Xie, L. & Hong, Y. Distributed optimal consensus of multiple double integrators under bounded velocity and acceleration. Control Theory Technol. 17, 85–98 (2019). https://doi.org/10.1007/s11768-019-8179-5

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  • DOI: https://doi.org/10.1007/s11768-019-8179-5

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