The relative order and inverses of recurrent networks (Q1911306)

Three types of recurrent network architectures (Hopfield network, and two structures with static nonlinearities and linear dynamic filters) are studied by using differential geometric methods. A number of theorems prove that these networks can be configured to provide finite relative order ranging from unity to the dimension of the state space of the architecture. Moreover, it is shown that such a recurrent network with finite relative order has a local inverse which is also a recurrent network and can be used in controller design based on the inverse model principle.