TY - GEN
T1 - Robust identification of uncertain schrodinger type complex partial differential equations
AU - Chairez, I.
AU - Fuentes, R.
AU - Poznyak, A.
AU - Poznyak, T.
PY - 2010
Y1 - 2010
N2 - Schrodinger equation is a well known example of the so-called complex partial differential equations (C-PDE). This paper presents a technique based in the Differential Neural Networks (DNN)methodology to solve the nonparametric identification problem of systems described by C-PDE. In this case, the identification scheme is proposed as the composition of two coupled DNN: the first one is used to approximate the real part of the complex valued equation and the second reproduces the complementary imaginary part. The convergence of the identification is obtained by a modified Lyapunov function in ininite dimensional spaces. The adaptive laws for complex weights ensure the convergence of the DNN trajectories to the sates of the PDE complex-valued. In order to investigate the qualitative behavior of the suggested technique, it is analyzed, as an example, the approximation of Schrodinger equation. The suggested no parametric identiier converge to the trajectories of the uncertain complex systems. This novel methodology that explores the application of the DNN method for the identiication of complex PDE has shown its ability to produce a numerical model of an uncertain complex valued system.
AB - Schrodinger equation is a well known example of the so-called complex partial differential equations (C-PDE). This paper presents a technique based in the Differential Neural Networks (DNN)methodology to solve the nonparametric identification problem of systems described by C-PDE. In this case, the identification scheme is proposed as the composition of two coupled DNN: the first one is used to approximate the real part of the complex valued equation and the second reproduces the complementary imaginary part. The convergence of the identification is obtained by a modified Lyapunov function in ininite dimensional spaces. The adaptive laws for complex weights ensure the convergence of the DNN trajectories to the sates of the PDE complex-valued. In order to investigate the qualitative behavior of the suggested technique, it is analyzed, as an example, the approximation of Schrodinger equation. The suggested no parametric identiier converge to the trajectories of the uncertain complex systems. This novel methodology that explores the application of the DNN method for the identiication of complex PDE has shown its ability to produce a numerical model of an uncertain complex valued system.
KW - Adaptive identification
KW - Complex partial differential equations
KW - Neural networks
UR - http://www.scopus.com/inward/record.url?scp=78650263655&partnerID=8YFLogxK
U2 - 10.1109/ICEEE.2010.5608635
DO - 10.1109/ICEEE.2010.5608635
M3 - Contribución a la conferencia
AN - SCOPUS:78650263655
SN - 9781424473120
T3 - Program and Abstract Book - 2010 7th International Conference on Electrical Engineering, Computing Science and Automatic Control, CCE 2010
SP - 170
EP - 175
BT - Program and Abstract Book - 2010 7th International Conference on Electrical Engineering, Computing Science and Automatic Control, CCE 2010
T2 - 2010 7th International Conference on Electrical Engineering, Computing Science and Automatic Control, CCE 2010
Y2 - 8 September 2010 through 10 September 2010
ER -