Advertisement

Cooperative Adaptive Control for Systems with Second-Order Nonlinear Dynamics

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

Abstract

In Chap. 8, we designed cooperative adaptive controllers for multi-agent systems having first-order nonlinear dynamics. In this chapter, we study adaptive control for cooperative multi-agent systems having second-order nonidentical nonlinear dynamics. The study of second-order and higher-order consensus is required to implement synchronization in most real-world applications such as formation control and coordination among unmanned aerial vehicles (UAVs), where both position and velocity must be controlled. Note that Lagrangian motion dynamics and robotic systems can be written in the form of second-order systems. Moreover, second-order integrator consensus design (as opposed to first-order integrator node dynamics) involves more details about the interaction between the system dynamics and control design problem and the graph structure as reflected in the Laplacian matrix. As such, second-order consensus is interesting because there one must confront more directly the interface between control systems and communication graph structure.

References

  1. 1.
    Das A, Lewis FL (2010) Distributed adaptive control for synchronization of unknown nonlinear networked systems. Automatica 46(12):2014–2021CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Das A, Lewis FL (2011) Cooperative adaptive control for synchronization of second-order systems with unknown nonlinearities. Int J Robust Nonlinear Control 21(13):1509–1524CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Ge SS, Wang C (2004) Adaptive neural control of uncertain MIMO nonlinear systems. IEEE Trans Neural Netw 15(3):674–692CrossRefGoogle Scholar
  4. 4.
    Ge SS, Hang CC, Zhang T (1998) Stable Adaptive Neural Network Control. Springer, BerlinGoogle Scholar
  5. 5.
    Hornik K, Stinchombe M, White H (1989) Multilayer feedforward networks are universal approximations. Neural Netw 2(5):359–366CrossRefGoogle Scholar
  6. 6.
    Khalil HK (2002) Nonlinear Systems, 3rd edn. Prentice Hall, Upper Saddle River, NJGoogle Scholar
  7. 7.
    Khoo S, Xie L, Man Z (2009) Robust finite-time consensus tracking algorithm for multirobot systems. IEEE Trans Mechatron 14(2):219–228CrossRefGoogle Scholar
  8. 8.
    Lewis FL, Yesildirek A, Liu K (1996) Multilayer neural net robot controller with guaranteed tracking performance. IEEE Trans Neural Netw 7(2):388–399CrossRefGoogle Scholar
  9. 9.
    Lewis FL, Jagannathan S, Yesildirek A (1999) Neural Network Control of Robot Manipulators and Nonlinear Systems. Taylor and Francis, LondonGoogle Scholar
  10. 10.
    Qu Z (2009) Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles. Springer-Verlag, New YorkGoogle Scholar
  11. 11.
    Stone MH (1948) The generalized weierstrass approximation theorem. Math Mag 21(4/5):167–184/237–254Google Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  • Frank L. Lewis
    • 1
  • 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

Personalised recommendations