THE RELATIVE ORDER AND INVERSES OF RECURRENT NETWORKS

Differential geometry is used to investigate the structure of neural-n etwork-based control systems. The key aspect is relative order-an inva riant property of dynamic systems. Finite relative order allows the sp ecification of a minimal architecture for a recurrent network. Any sys tem with finite relative order has a left inverse. It is shown that a recurrent network with finite relative order has a local inverse that is also a recurrent network with the same weights. The results have im plications for the use of recurrent networks in the inverse-model-base d control of nonlinear systems.