The Relative Order and Inverses of Recurrent Networks

In this paper differential geometry is used to investigate the structure of neural network based control systems. The key aspect is relative order, an invariant property, of dynamic systems. Finite relative order allows the specification of a minimal architecture for a recurrent network. Any system with finite relative order has a leftinverse. 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 implications for the use of recurrent networks in the inverse model based control of nonlinear systems