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 N. Johnson

Research output: Contribution to journalArticlepeer-review


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
Issue number7
StatePublished - 2012
Externally publishedYes


  • Adaptive control
  • kernel
  • nonlinear control systems
  • radial basis function (RBF) networks

ASJC Scopus subject areas

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


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