@article{7f4a38f9ebbe458d8a91382b844795d6,

title = "State observability in recurrent neural networks",

abstract = "We obtain a characterization of observability for a class of nonlinear systems which appear in neural networks research.",

keywords = "Recurrent neural networks, observability",

author = "Francesca Albertini and Sontag, {Eduardo D.}",

note = "Funding Information: to each coordinate of an n-vector, a(Xl ..... x,) = (a(xl) ..... a(x,)). See Figure 1 for a block diagram, where A indicates either a unit delay or integration. The complete model is specified once that a and the triple (A, B, C) are given. (In continuous time, one needs to assume also that a is at least locally Lipschitz, so that existence and local uniqueness of the differential equation holds.) Many questions, mirroring those for linear systems (for which a is the identity) can be posed. In the recent work \[1\]w, e explored realization questions, and in particular the fact that all the entries of the matrices A, B, and C can be recovered (up to a small number of symmetries) from the zero-initial state input/output behavior, assuming suitable minimality assumptions, and as long as a is nonlinear enough. This is somewhat surprising, since for the linear case one can only recover the parameters up to basis changes, and it is reminiscent of old work of Rugh and coworkers, as well as Boyd and Chua (see for instance \[5, 3\]) on uniqueness of interconnections containing nonlinearities. (Reference I-2\] explains the relation between those more classical facts and the result in \[1\].) Correspondence to.{"} Prof. E.D. Sontag, Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA. E-mail: sontag@control.rutgers.edu. * This research was supported in part by US Air Force Grant AFOSR-91-0346, and also by an INDAM (Istituto Nazionale di Alta Matematica Francesco Severi, Italy) fellowship. ** Also: Universita' di Padova, Dipartimento di Matematica, Via Belzoni 7, 35100 Padova, Italy.",

year = "1994",

month = apr,

doi = "10.1016/0167-6911(94)90054-X",

language = "English (US)",

volume = "22",

pages = "235--244",

journal = "Systems and Control Letters",

issn = "0167-6911",

publisher = "Elsevier",

number = "4",

}