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: Contribution to journalArticle

34 Citations (Scopus)

Abstract

Classical work in model reference adaptive control for uncertain nonlinear dynamical systems with a radial basis function (RBF) neural network adaptive element does not guarantee that the network weights stay bounded in a compact neighborhood of the ideal weights when the system signals are not persistently exciting (PE). Recent work has shown, however, that an adaptive controller using specifically recorded data concurrently with instantaneous data guarantees boundedness without PE signals. However, the work assumes fixed RBF network centers, which requires domain knowledge of the uncertainty. Motivated by reproducing kernel Hilbert space theory, we propose an online algorithm for updating the RBF centers to remove the assumption. In addition to proving boundedness of the resulting neuro-adaptive controller, a connection is made between PE signals and kernel methods. Simulation results show improved performance.

Original languageEnglish (US)
Article number6208915
Pages (from-to)1130-1141
Number of pages12
JournalIEEE Transactions on Neural Networks and Learning Systems
Volume23
Issue number7
DOIs
StatePublished - Dec 1 2012

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Hilbert spaces
Model reference adaptive control
Nonlinear dynamical systems
Controllers
Signal systems
Radial basis function networks
Neural networks
Uncertainty

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence

Cite this

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Reproducing kernel hilbert space approach for the online update of radial bases in neuro-adaptive control. / Kingravi, Hassan A.; Chowdhary, Girish; Vela, Patricio A.; Johnson, Eric.

In: IEEE Transactions on Neural Networks and Learning Systems, Vol. 23, No. 7, 6208915, 01.12.2012, p. 1130-1141.

Research output: Contribution to journalArticle

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