TY - JOUR
T1 - Adaptive identifier for uncertain complex nonlinear systems based on continuous neural networks
AU - Alfaro-Ponce, Mariel
AU - Cruz, Amadeo Arguelles
AU - Chairez, Isaac
PY - 2014/3
Y1 - 2014/3
N2 - This paper presents the design of a complex-valued differential neural network identifier for uncertain nonlinear systems defined in the complex domain. This design includes the construction of an adaptive algorithm to adjust the parameters included in the identifier. The algorithm is obtained based on a special class of controlled Lyapunov functions. The quality of the identification process is characterized using the practical stability framework. Indeed, the region where the identification error converges is derived by the same Lyapunov method. This zone is defined by the power of uncertainties and perturbations affecting the complex-valued uncertain dynamics. Moreover, this convergence zone is reduced to its lowest possible value using ideas related to the so-called ellipsoid methodology. Two simple but informative numerical examples are developed to show how the identifier proposed in this paper can be used to approximate uncertain nonlinear systems valued in the complex domain.
AB - This paper presents the design of a complex-valued differential neural network identifier for uncertain nonlinear systems defined in the complex domain. This design includes the construction of an adaptive algorithm to adjust the parameters included in the identifier. The algorithm is obtained based on a special class of controlled Lyapunov functions. The quality of the identification process is characterized using the practical stability framework. Indeed, the region where the identification error converges is derived by the same Lyapunov method. This zone is defined by the power of uncertainties and perturbations affecting the complex-valued uncertain dynamics. Moreover, this convergence zone is reduced to its lowest possible value using ideas related to the so-called ellipsoid methodology. Two simple but informative numerical examples are developed to show how the identifier proposed in this paper can be used to approximate uncertain nonlinear systems valued in the complex domain.
KW - Complex-valued neural networks
KW - continuous neural network
KW - controlled Lyapunov function
KW - nonparametric identifier
UR - http://www.scopus.com/inward/record.url?scp=84896875913&partnerID=8YFLogxK
U2 - 10.1109/TNNLS.2013.2275959
DO - 10.1109/TNNLS.2013.2275959
M3 - Artículo
C2 - 24807445
SN - 2162-237X
VL - 25
SP - 483
EP - 494
JO - IEEE Transactions on Neural Networks and Learning Systems
JF - IEEE Transactions on Neural Networks and Learning Systems
IS - 3
M1 - 6585821
ER -