Control Theory and Technology

, Volume 17, Issue 1, pp 85–98 | Cite as

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

  • Zhirong Qiu
  • Lihua XieEmail author
  • Yiguang Hong


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.


Distributed optimization double integrators bounded velocity bounded input 


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Copyright information

© Editorial Board of Control Theory & Applications, South China University of Technology and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Electrical and Electronic EngineeringNanyang Technological UniversitySingaporeSingapore
  2. 2.Key Laboratory of Systems and Control, Institute of Systems ScienceChinese Academy of SciencesBeijingChina

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