Cooperative Adaptive Control for Systems with First-Order Nonlinear Dynamics

  • Frank L. LewisEmail author
  • Hongwei Zhang
  • Kristian Hengster-Movric
  • Abhijit Das
Part of the Communications and Control Engineering book series (CCE)


In cooperative control systems, the control protocol for each agent is allowed to depend only on information about itself and its neighbors in the graph topology. We have confronted this problem for optimal cooperative control design in Part I of the book. In cooperative adaptive control systems, there is an additional problem. In adaptive control systems, the control law depends on unknown parameters that are tuned online in real time to improve the performance of the controller, whereas the challenge in cooperative adaptive control is to make sure that both the control protocols and the parameter tuning laws are distributed in terms of the allowed graph topology. That is, they are allowed to depend only on locally available information about the agent and its neighbors. We shall see in this chapter that the key to the design of distributed adaptive tuning algorithms is the selection of suitable Lyapunov functions that depend on the graph topology. This is closely connected to the selection of global performance indices that depend on the graph topology in Chap.  5. The basis for the selection of suitable graph-dependent Lyapunov functions was laid in the discussion on the graph Laplacian potential in Chap.  7.


Tuning Law Cooperative Control System Global Performance Index Distributed Control Protocol Graph Topology 
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Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  • Frank L. Lewis
    • 1
    Email author
  • Hongwei Zhang
    • 2
  • Kristian Hengster-Movric
    • 3
  • Abhijit Das
    • 4
  1. 1.UTA Research InstituteUniversity of Texas at ArlingtonFort WorthUSA
  2. 2.School of Electrical EngineeringSouthwest Jiaotong UniversityChengduChina, People’s Republic
  3. 3.UTA Research InstituteUniversity of Texas at ArlingtonFort WorthUSA
  4. 4.Advanced Systems Engineering​Danfoss Power Solutions (US) Company​AmesUSA

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