TY - JOUR

T1 - State observability in recurrent neural networks

AU - Albertini, Francesca

AU - Sontag, Eduardo D.

N1 - 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: [email protected]. * 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.

PY - 1994/4

Y1 - 1994/4

N2 - We obtain a characterization of observability for a class of nonlinear systems which appear in neural networks research.

AB - We obtain a characterization of observability for a class of nonlinear systems which appear in neural networks research.

KW - Recurrent neural networks

KW - observability

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U2 - 10.1016/0167-6911(94)90054-X

DO - 10.1016/0167-6911(94)90054-X

M3 - Article

AN - SCOPUS:0028417030

SN - 0167-6911

VL - 22

SP - 235

EP - 244

JO - Systems and Control Letters

JF - Systems and Control Letters

IS - 4

ER -