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 Citations (Scopus)

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
StatePublished - 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

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

Fingerprint

Reproducing Kernel Hilbert Space
Hilbert spaces
Adaptive Control
Update
Model reference adaptive control
Nonlinear dynamical systems
Controllers
Signal systems
Radial basis function networks
Boundedness
Model Reference Adaptive Control
Neural networks
Controller
Radial Basis Function Network
Radial Basis Function Neural Network
Kernel Methods
Nonlinear Dynamical Systems
Online Algorithms
Domain Knowledge
Radial Functions

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] https://doi.org/10.1109/CDC.2011.6160765
Kingravi, Hassan A. ; Chowdhary, Girish ; Vela, Patricio A. ; Johnson, Eric. / A reproducing Kernel Hilbert Space approach for the online update of Radial Bases in neuro-adaptive control. 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. 2011. pp. 1796-1802
@inproceedings{43153e48dadb41648a3eb51d240918b4,
title = "A reproducing Kernel Hilbert Space approach for the online update of Radial Bases in neuro-adaptive control",
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.",
author = "Kingravi, {Hassan A.} and Girish Chowdhary and Vela, {Patricio A.} and Eric Johnson",
year = "2011",
month = "12",
day = "1",
doi = "10.1109/CDC.2011.6160765",
language = "English (US)",
isbn = "9781612848006",
pages = "1796--1802",
booktitle = "2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011",

}

Kingravi, HA, Chowdhary, G, Vela, PA & 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., 6160765, pp. 1796-1802, 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011, Orlando, FL, United States, 12/12/11. https://doi.org/10.1109/CDC.2011.6160765

A 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.

2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011. 2011. p. 1796-1802 6160765.

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

TY - GEN

T1 - A reproducing Kernel Hilbert Space approach for the online update of Radial Bases in neuro-adaptive control

AU - Kingravi, Hassan A.

AU - Chowdhary, Girish

AU - Vela, Patricio A.

AU - Johnson, Eric

PY - 2011/12/1

Y1 - 2011/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84860699436&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84860699436&partnerID=8YFLogxK

U2 - 10.1109/CDC.2011.6160765

DO - 10.1109/CDC.2011.6160765

M3 - Conference contribution

SN - 9781612848006

SP - 1796

EP - 1802

BT - 2011 50th IEEE Conference on Decision and Control and European Control Conference, CDC-ECC 2011

ER -

Kingravi HA, Chowdhary G, Vela PA, Johnson E. 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. 2011. p. 1796-1802. 6160765 https://doi.org/10.1109/CDC.2011.6160765