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                      EE-SYSTEMS DEPARTMENT
                            CONTROLS



        Neural Networks for Dynamical System Identification
           and Their Application in Virtual Reality


                                by


                     Manolis A. Christodoulou


         Department of Electronic & Computer Engineering
                 Technical University of Crete
                     Chania 73100, GREECE


                             Abstract


The capabilities of Recursive High Order Neural Networks (RHONN) are
investigated.  These networks can learn and behave like unknown
dynamical systems.  First the properties of general RHONN models are
investigated, which are used in order to approximate and learn
the behaviour of nonlinear dynamical systems.  The main result is
that, under some very mild assumptions, for a very generic class of
nonlinear dynamical systems and for any degree of accuracy, there
exist RHONN's that can approximate the systems in the above class.
Moreover, learning laws are proposed and mathematically analyzed, for
the adjustment of the RHONN synaptic weights.  Using the synaptic weights linear-in-the parameters
property, it is proved that the learning laws ensure error stability,
convergence, and robustness.
Next, the properties of a special class of RHONNs the symmetric
RHONN's (s-RHONN) are investigated.  s-RHONN's are gradient dynamical
systems and therefore their stability properties can be easily
investigated.  Moreover, they are and they remain stable when either
bounded additive or multiplicative stochastic disturbances affect
their dynamics.


		 DATE:	 Friday, January 15, 1993

		 TIME:   2 P.M. SEMINAR

		 LOCATION: EEB248

		 HOST:	 Prof. Petros Ioannou

		         (213)740-4452