Space-Frequency Localized Basis Function Networks for Nonlinear System Estimation and Control


Space-Frequency Localized Basis Function Networks for Nonlinear System Estimation and Control, M. Cannon and J.J.E. Slotine, Neurocomputing, 9(3), 1995.


Stable neural network control and estimation may be viewed formally as a merging of concepts from nonlinear dynamic systems theory with tools from multivariate approximation theory. This paper extends earlier results on adaptive control and estimation of nonlinear systems using gaussian radial basis functions to the on-line generation of irregularly sampled networks, using tools from multiresolution analysis and wavelet theory. This yields much more compact and efficient system representations while preserving global closed-loop stability.

Approximation models employing basis functions that are localized in both space and spatial frequency admit a measure of the approximated function's spatial frequency content that is not directly dependent on reconstruction error. As a result, these models afford a means of adaptively selecting basis functions according to the local spatial frequency content of the approximated function. An algorithm for stable, on-line adaptation of output weights simultaneously with node configuration in a class of non-parametric models with wavelet basis functions is presented. An asymptotic bound on the error in the network's reconstruction is derived and shown to be dependent solely on the minimum approximation error associated with the steady state node configuration. In addition, prior bounds on the temporal bandwidth of the system to be identified or controlled are used to develop a criterion for on-line selection of radial and ridge wavelet basis functions, thus reducing the rate of increase in network's size with the dimension of the state vector.

Experimental results obtained by using the network to predict the path of an unknown light bluff object thrown through air, in an active-vision based robotic catching system, are given to illustrate the network's performance in a simple real-time application.

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