The relative order and inverses of recurrent networks
Kambhampati, C., Manchanda, S., Delgado, A., Green, G. R. R., Warwick, K. and Tham, M. (1996) The relative order and inverses of recurrent networks. Automatica, 32 (1). pp. 117-123. ISSN 0005-1098
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To link to this article DOI: 10.1016/0005-1098(95)00098-4
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 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 implications for the use of recurrent networks in the inverse-model-based control of nonlinear systems.