TY - JOUR
T1 - On affine state-space neural networks for system identification: Global stability conditions and complexity management
AU - Gil, Paulo José Carrilho de Sousa
AU - Henriques, Jorge H.
AU - Cardoso, Alberto J.L.
AU - Dourado, Antonio
N1 - O PDF é a versão da editora, mas esta permite o auto arquivo desta versão 3 meses após a publicação.
Salima Rehemtula
PY - 2013/1/1
Y1 - 2013/1/1
N2 - A nonlinear black box structure represented by an affine three-layered state-space neural network with exogenous inputs is considered for nonlinear systems identification. Global stability conditions are derived based on Lyapunov’s stability theory and on the contraction mapping theorem. The problem of structural complexity is also addressed by defining an upper bound for the number of hidden layer neurons expressed as the cardinality of the dominant singular values of the oblique subspace projection of data driven Hankel matrices. Rank degeneracy stemming from nonlinearities, colored noise or finite data sets are dealt with either in terms of the sensitivity of singular values or by comparing the relevance of including additional coordinates in a given realization. Two examples are provided for illustrating the feasibility of derived global stability condition and the proposed approach for delaying with the complexity problem.
AB - A nonlinear black box structure represented by an affine three-layered state-space neural network with exogenous inputs is considered for nonlinear systems identification. Global stability conditions are derived based on Lyapunov’s stability theory and on the contraction mapping theorem. The problem of structural complexity is also addressed by defining an upper bound for the number of hidden layer neurons expressed as the cardinality of the dominant singular values of the oblique subspace projection of data driven Hankel matrices. Rank degeneracy stemming from nonlinearities, colored noise or finite data sets are dealt with either in terms of the sensitivity of singular values or by comparing the relevance of including additional coordinates in a given realization. Two examples are provided for illustrating the feasibility of derived global stability condition and the proposed approach for delaying with the complexity problem.
KW - Global stability conditions
KW - Complexity management
KW - Oblique projections
KW - Affine state-space neural networks
KW - Singular value decomposition
KW - Affine state-space neural networks
KW - Complexity management
KW - Global stability conditions
KW - Oblique projections
KW - Singular value decomposition
U2 - 10.1016/j.conengprac.2012.11.008
DO - 10.1016/j.conengprac.2012.11.008
M3 - Article
VL - 21
SP - 518
EP - 529
JO - Control Engineering Practice
JF - Control Engineering Practice
SN - 0967-0661
IS - 4
ER -