Nonlinear \({\mathcal{H}}_{\varvec\infty}\) Control

  • Adriano A. G. Siqueira
  • Marco H. Terra
  • Marcel Bergerman


This chapter deals with nonlinear \({\mathcal{H}}_{\infty}\) control methodologies for robot manipulators. The nonlinear \({\mathcal{H}}_{\infty}\) control considered guarantees an appropriate attenuation of the torque disturbance effect on the joint positions. We deal with two fundamental approaches for this class of controllers; the first is based on game theory and the second is based on linear parameter-varying (LPV) techniques. We provide solutions based on state and output feedback controls.


Game Theory Linear Matrix Inequality Robot Manipulator Weighting Matrice Cholesky Factorization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Apkarian P, Adams RJ (1998) Advanced gain-scheduling techniques for uncertain systems. IEEE Trans Control Syst Technol 6(1):21–32CrossRefGoogle Scholar
  2. 2.
    Basar T, Bernhard P (1990) \({\mathcal{H}}_{\infty}\)-Optimal control and related minimax problems. Birkhauser, BerlinGoogle Scholar
  3. 3.
    Chen BS, Chang YC (1997) Nonlinear mixed \({\mathcal{H}}_{2} / {\mathcal{H}}_{\infty}\) control for robust tracking design of robotic systems. Int J Control 67(6):837–857MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Chen BS, Lee TS, Feng JH (1994) A nonlinear \({\mathcal{H}}_{\infty}\) control design in robotic systems under parameter perturbation and external disturbance. Int J Control 59(2):439–461MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Gahinet P, Apkarian P (1994) A linear matrix inequality approach to \({\mathcal{H}}_\infty\) control. Int J Robust Nonlinear Control 4(4):421–448MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Gahinet P, Nemiroviski A, Laub AJ, Chilali M (1995) LMI control toolbox. The MathWorks, Inc., NatickGoogle Scholar
  7. 7.
    Johansson R (1990) Quadratic optimization of motion coordination and control. IEEE Trans Autom Control 35(11):1197–1208MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Postlethwaite I, Bartoszewicz A (1998) Application of non-linear \({\mathcal{H}}_{\infty}\) control to the tetrabot robot manipulator. Proc Inst Mech Eng: Part I. J Syst Control Eng 212(16):459–465CrossRefGoogle Scholar
  9. 9.
    Wu F, Yang XH, Packard A, Becker G (1996) Induced \({\mathcal{L}}_2\)-norm control for LPV systems with bounded parameter variation rates. Int J Robust Nonlinear Control 6(9–10):983–998MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  • Adriano A. G. Siqueira
    • 1
  • Marco H. Terra
    • 1
  • Marcel Bergerman
    • 2
  1. 1.Engineering School of São CarlosUniversity of São PauloSão CarlosBrazil
  2. 2.CMU Robotics InstitutePittsburghUSA

Personalised recommendations