A reproducing Kernel Hilbert Space approach for the online update of Radial Bases in neuro-adaptive control

Hassan A. Kingravi, Girish Chowdhary, Patricio A. Vela, Eric Johnson

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

Classical gradient based adaptive laws in model reference adaptive control for uncertain nonlinear dynamical systems with a Radial Basis Function (RBF) neural networks adaptive element do not guarantee that the network weights stay bounded in a compact neighborhood of the ideal weights without Persistently Exciting (PE) system signals or a-priori known bounds on ideal weights. Recent work has shown, however, that an adaptive controller using specifically recorded data concurrently with instantaneous data can guarantee such boundedness without requiring PE signals. However, in this work, the assumption has been that the RBF network centers are fixed, which requires some domain knowledge of the uncertainty. We employ a Reproducing Kernel Hilbert Space theory motivated online algorithm for updating the RBF centers to remove this assumption. Along with showing the boundedness of the resulting neuro-adaptive controller, a connection is also made between PE signals and kernel methods. Simulation results show improved performance.

Original languageEnglish (US)
Title of host publication2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
Pages1796-1802
Number of pages7
DOIs
Publication statusPublished - Dec 1 2011
Event2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 - Orlando, FL, United States
Duration: Dec 12 2011Dec 15 2011

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011
CountryUnited States
CityOrlando, FL
Period12/12/1112/15/11

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All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

Cite this

Kingravi, H. A., Chowdhary, G., Vela, P. A., & Johnson, E. (2011). A reproducing Kernel Hilbert Space approach for the online update of Radial Bases in neuro-adaptive control. In 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011 (pp. 1796-1802). [6160765] (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2011.6160765