A parameter optimization method for radial basis function type models

This paper considers the nonlinear systems modeling problem for control. A structured nonlinear parameter optimization method (SNPOM) adapted to radial basis function (RBF) networks and an RBF network-style coefficients autoregressive model with exogenous variable model parameter estimation is presented. This is an off-line nonlinear model parameter optimization method, depending partly on the Levenberg-Marquardt method for nonlinear parameter optimization and partly on the least-squares method using singular value decomposition for linear parameter estimation. When compared with some other algorithms, the SNPOM accelerates the computational convergence of the parameter optimization search process of RBF-type models. The usefulness of this approach is illustrated by means of several examples.

[1]  H. Akaike.  A new look at the statistical model identification , 1974 .

[2]  Thomas F. Coleman,et al.  An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds , 1993, SIAM J. Optim..

[3]  Tohru Ozaki,et al.  Reconstructing the Nonlinear Dynamics of Epilepsy Data Using Nonlinear Time series Analysis , 1999 .

[4]  George W. Irwin,et al.  A hybrid linear/nonlinear training algorithm for feedforward neural networks , 1998, IEEE Trans. Neural Networks.

[5]  Shang-Liang Chen,et al.  Orthogonal least squares learning algorithm for radial basis function networks , 1991, IEEE Trans. Neural Networks.

[6]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[7]  M. Priestley.  STATE‐DEPENDENT MODELS: A GENERAL APPROACH TO NON‐LINEAR TIME SERIES ANALYSIS , 1980 .

[8]  E. Swidenbank,et al.  A Local Model Networks Based Multivariable Long-Range Predictive Control Strategy for Thermal Power Plants , 1998, Autom..

[9]  Aaas News,et al.  Book Reviews , 1893, Buffalo Medical and Surgical Journal.

[10]  Andrew A. Goldenberg,et al.  Learning approximation of feedforward control dependence on the task parameters with application to direct-drive manipulator tracking , 1997, IEEE Trans. Robotics Autom..

[11]  Sheng Chen,et al.  Non-linear systems identification using radial basis functions , 1990 .

[12]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[13]  Gene H. Golub,et al.  Matrix computations , 1983 .

[14]  Jean-Marc Vesin,et al.  An amplitude-dependent autoregressive model based on a radial basis functions expansion , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[15]  John Moody,et al.  Fast Learning in Networks of Locally-Tuned Processing Units , 1989, Neural Computation.

[16]  D. Gorinevsky.  An approach to parametric nonlinear least square optimization and application to task-level learning control , 1997, IEEE Trans. Autom. Control..

[17]  T. Ozaki,et al.  Modelling nonlinear random vibrations using an amplitude-dependent autoregressive time series model , 1981 .

[18]  George W. Irwin,et al.  Fast parallel off-line training of multilayer perceptrons , 1997, IEEE Trans. Neural Networks.

[19]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[20]  Zhaoyun Shi,et al.  Nonlinear time series modelling with the radial basis function-based state-dependent autoregressive model , 1999, Int. J. Syst. Sci..

[21]  D. Marquardt.  An Algorithm for Least-Squares Estimation of Nonlinear Parameters , 1963 .

[22]  Thomas F. Coleman,et al.  Optimization Toolbox User's Guide , 1998 .