Narendra's stability proof

[sontag@control.rutgers.edu]

   From: Russell Leighton <russ at oceanus.mitre.org>
   At IJCNN `91 Narendra spoke of a paper where
   he has proven stability for a control system
   using backpropagation neural networks.
   Does anyone know where this was published?
   Thanks.
   Russ

At the American Automatic Control Conference, three weeks ago in Boston, there
were a few papers dealing with adaptive control using neural nets. Among them:

    TA1:    
    8:30-9:00
    Intelligent Control Using Neural Networks
    Narendra, K., Yale University
    Mukhopadhyay, S., Yale University
    
    TP1:
    17:30-18:00
    Regulation of Nonlinear Dynamical Systems Using Neural
    Networks
    Narendra, K., Yale University
    Levine, A., Yale University
    
    FA1:    
    11:15-11:45
    Gradient Methods for Learning in Dynamical System
    Containing Neural Networks
    Narendra, K., Yale University
    Parthasarathy, K., Yale University
    
    12:15-12:45
    Stability and Convergence Issues in Neural Network Control
    Slotine, J., Massachusetts Institute of Technology

As far as I recall, all results on stability dealt with RADIAL-BASIS types of
networks, assuming FIXED centers, so the estimation problem is a LINEAR one.
The paper of Slotine has a nice technique for estimating weights at the lower
level, using spectral information on the training data (I guess in the same
spirit that others would use clustering).   Before the conference, there was a
one-day course, organized by Narendra, which covered neural net approaches to
control; he had a writeup prepared for that, which might cover the stability
results (I don't know, nor do I know how you can get a copy).

The email addresses for Slotine and Narendra are as follows:

    jjs at athena.mit.edu (Jean-Jacques Slotine, Mech Engr, MIT)
    narendra at bart.eng.yale.edu (Narendra, Engineering, Yale)

-eduardo
PS: My paper in the same proceedings, WP9: "Feedback Stabilization Using
Two-Hidden-Layer Nets", covered the results on why *TWO* hidden layers are
needed for control (and some other) problems, rather than one.  (A tech report
was posted late last year to neuroprose, covering the contents of this paper.)