TY - JOUR
T1 - Wavelet differential neural network observer
AU - Chairez, Isaac
PY - 2009
Y1 - 2009
N2 - State estimation for uncertain systems affected by external noises is an important problem in control theory. This paper deals with a state observation problem when the dynamic model of a plant contains uncertainties or it is completely unknown. Differential neural network (NN) approach is applied in this uninformative situation but with activation functions described by wavelets. A new learning law, containing an adaptive adjustment rate, is suggested to imply the stability condition for the free parameters of the observer. Nominal weights are adjusted during the preliminary training process using the least mean square (LMS) method. Lyapunov theory is used to obtain the upper bounds for the weights dynamics as well as for the mean squared estimation error. Two numeric examples illustrate this approach: first, a nonlinear electric system, governed by the Chua's equation and second the Lorentz oscillator. Both systems are assumed to be affected by external perturbations and their parameters are unknown.
AB - State estimation for uncertain systems affected by external noises is an important problem in control theory. This paper deals with a state observation problem when the dynamic model of a plant contains uncertainties or it is completely unknown. Differential neural network (NN) approach is applied in this uninformative situation but with activation functions described by wavelets. A new learning law, containing an adaptive adjustment rate, is suggested to imply the stability condition for the free parameters of the observer. Nominal weights are adjusted during the preliminary training process using the least mean square (LMS) method. Lyapunov theory is used to obtain the upper bounds for the weights dynamics as well as for the mean squared estimation error. Two numeric examples illustrate this approach: first, a nonlinear electric system, governed by the Chua's equation and second the Lorentz oscillator. Both systems are assumed to be affected by external perturbations and their parameters are unknown.
KW - Continuous systems
KW - Learning schemes
KW - Neural network (NN)
KW - Sliding-mode observers
KW - State estimation
KW - Wavelet approximation
UR - http://www.scopus.com/inward/record.url?scp=70349236879&partnerID=8YFLogxK
U2 - 10.1109/TNN.2009.2024203
DO - 10.1109/TNN.2009.2024203
M3 - Artículo
C2 - 19674951
SN - 1045-9227
VL - 20
SP - 1439
EP - 1449
JO - IEEE Transactions on Neural Networks
JF - IEEE Transactions on Neural Networks
IS - 9
ER -