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Optimal NPID Stabilization of Linear Systems

Author

Listed:
  • B. Armstrong

    (University of Wisconsin-Milwaukee)

  • I. Lauko

    (University of Wisconsin-Milwaukee)

  • B. Wade

    (University of Wisconsin- Milwaukee)

Abstract

We consider the problem of finding the optimal, robust stabilization of linear systems within a family of nonlinear feedback laws. Investigation of the efficiency of full-state based and partial-state based so-called NPID feedback schemes proposed for the stabilization of systems in robotic applications has provided the motivation for our work. We prove that, for a given quadratic Lyapunov function and a given family of nonlinear feedback laws, there exist optimal piecewise linear feedbacks that make the generalized Lyapunov derivative of the closed-loop system minimal. The result provides improved stabilization over the nonlinear stabilizing feedback law proposed in Ref. 1 as demonstrated in simulations of the Sarcos Dextrous Manipulator.

Suggested Citation

  • B. Armstrong & I. Lauko & B. Wade, 2005. "Optimal NPID Stabilization of Linear Systems," Journal of Optimization Theory and Applications, Springer, vol. 124(2), pages 307-322, February.
    • Handle: RePEc:spr:joptap:v:124:y:2005:i:2:d:10.1007_s10957-004-0927-z
    DOI: 10.1007/s10957-004-0927-z
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