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Feedback error learning and nonlinear adaptive control




In this paper, we present our theoretical investigations of the technique of feedback error learning (FEL) from the viewpoint of adaptive control. We first discuss the relationship between FEL and nonlinear adaptive control with adaptive feedback linearization, and show that FEL can be interpreted as a form of nonlinear adaptive control. Second, we present a Lyapunov analysis suggesting that the condition of strictly positive realness (SPR) associated with the tracking error dynamics is a sufficient condition for asymptotic stability of the closed-loop dynamics. Specifically, for a class of second order SISO systems, we show that this condition reduces to KD^2 > KP; where KP and KD are positive position and velocity feedback gains, respectively. Moreover, we provide a ÔpassivityÕ-based stability analysis which suggests that SPR of the tracking error dynamics is a necessary and sufficient condition for asymptotic hyperstability. Thus, the condition KD^2>KP mentioned above is not only a sufficient but also necessary condition to guarantee asymptotic hyperstability of FEL, i.e. the tracking error is bounded and asymptotically converges to zero. As a further point, we explore the adaptive control and FEL framework for feedforward control formulations, and derive an additional sufficient condition for asymptotic stability in the sense of Lyapunov. Finally, we present numerical simulations to illustrate the stability properties of FEL obtained from our mathematical analysis.

Author(s): Nakanishi, J. and Schaal, S.
Book Title: Neural Networks
Volume: 17
Number (issue): 10
Pages: 1453-1465
Year: 2004

Department(s): Autonomous Motion
Bibtex Type: Article (article)

Cross Ref: p1806
Note: clmc
URL: http://www-clmc.usc.edu/publications/N/nakanishi-NN2004.pdf


  title = {Feedback error learning and nonlinear adaptive control},
  author = {Nakanishi, J. and Schaal, S.},
  booktitle = {Neural Networks},
  volume = {17},
  number = {10},
  pages = {1453-1465},
  year = {2004},
  note = {clmc},
  crossref = {p1806},
  url = {http://www-clmc.usc.edu/publications/N/nakanishi-NN2004.pdf}