TY - JOUR
T1 - Adaptive Neural Network Nonparametric Identifier with Normalized Learning Laws
AU - Chairez, Isaac
N1 - Publisher Copyright:
© 2016 IEEE.
PY - 2017/5
Y1 - 2017/5
N2 - This paper addresses the design of a normalized convergent learning law for neural networks (NNs) with continuous dynamics. The NN is used here to obtain a nonparametric model for uncertain systems described by a set of ordinary differential equations. The source of uncertainties is the presence of some external perturbations and poor knowledge of the nonlinear function describing the system dynamics. A new adaptive algorithm based on normalized algorithms was used to adjust the weights of the NN. The adaptive algorithm was derived by means of a nonstandard logarithmic Lyapunov function (LLF). Two identifiers were designed using two variations of LLFs leading to a normalized learning law for the first identifier and a variable gain normalized learning law. In the case of the second identifier, the inclusion of normalized learning laws yields to reduce the size of the convergence region obtained as solution of the practical stability analysis. On the other hand, the velocity of convergence for the learning laws depends on the norm of errors in inverse form. This fact avoids the peaking transient behavior in the time evolution of weights that accelerates the convergence of identification error. A numerical example demonstrates the improvements achieved by the algorithm introduced in this paper compared with classical schemes with no-normalized continuous learning methods. A comparison of the identification performance achieved by the no-normalized identifier and the ones developed in this paper shows the benefits of the learning law proposed in this paper.
AB - This paper addresses the design of a normalized convergent learning law for neural networks (NNs) with continuous dynamics. The NN is used here to obtain a nonparametric model for uncertain systems described by a set of ordinary differential equations. The source of uncertainties is the presence of some external perturbations and poor knowledge of the nonlinear function describing the system dynamics. A new adaptive algorithm based on normalized algorithms was used to adjust the weights of the NN. The adaptive algorithm was derived by means of a nonstandard logarithmic Lyapunov function (LLF). Two identifiers were designed using two variations of LLFs leading to a normalized learning law for the first identifier and a variable gain normalized learning law. In the case of the second identifier, the inclusion of normalized learning laws yields to reduce the size of the convergence region obtained as solution of the practical stability analysis. On the other hand, the velocity of convergence for the learning laws depends on the norm of errors in inverse form. This fact avoids the peaking transient behavior in the time evolution of weights that accelerates the convergence of identification error. A numerical example demonstrates the improvements achieved by the algorithm introduced in this paper compared with classical schemes with no-normalized continuous learning methods. A comparison of the identification performance achieved by the no-normalized identifier and the ones developed in this paper shows the benefits of the learning law proposed in this paper.
KW - Learning laws
KW - Logarithmic Lyapunov functions (LLFs)
KW - Nonparametric identifier
KW - Normalized adaptive laws
UR - http://www.scopus.com/inward/record.url?scp=84963656382&partnerID=8YFLogxK
U2 - 10.1109/TNNLS.2015.2505090
DO - 10.1109/TNNLS.2015.2505090
M3 - Artículo
C2 - 27076469
SN - 2162-237X
VL - 28
SP - 1216
EP - 1227
JO - IEEE Transactions on Neural Networks and Learning Systems
JF - IEEE Transactions on Neural Networks and Learning Systems
IS - 5
M1 - 7447821
ER -