TY - GEN
T1 - Neural network identication of uncertain 2d partial differential equations
AU - Chairez, I.
AU - Fuentes, R.
AU - Poznyak, A.
AU - Poznyak, T.
AU - Escudero, M.
AU - Viana, L.
PY - 2009
Y1 - 2009
N2 - There are many examples in science and engineering which are reduced to a set of partial differential equations (PDE's) through a process of mathematical modeling. Nevertheless there exist many sources of uncertainties around the aforementioned mathematical representation. It is well known that neural networks can approximate a large set of continuous functions defined on a compact set to an arbitrary accuracy. In this paper a strategy based on DNN for the non parametric identification of a mathematical model described by a class of two dimensional (2D) partial differential equations is proposed. The adaptive laws for weights ensure the "practical stability" of the DNN trajectories to the parabolic 2D-PDE states. To verify the qualitative behavior of the suggested methodology, here a non parametric modeling problem for a distributed parameter plant is analyzed.
AB - There are many examples in science and engineering which are reduced to a set of partial differential equations (PDE's) through a process of mathematical modeling. Nevertheless there exist many sources of uncertainties around the aforementioned mathematical representation. It is well known that neural networks can approximate a large set of continuous functions defined on a compact set to an arbitrary accuracy. In this paper a strategy based on DNN for the non parametric identification of a mathematical model described by a class of two dimensional (2D) partial differential equations is proposed. The adaptive laws for weights ensure the "practical stability" of the DNN trajectories to the parabolic 2D-PDE states. To verify the qualitative behavior of the suggested methodology, here a non parametric modeling problem for a distributed parameter plant is analyzed.
KW - Adaptive identification
KW - Distributed parameter systems
KW - Neural networks
KW - Partial differential equations and practical stability
UR - http://www.scopus.com/inward/record.url?scp=77949780965&partnerID=8YFLogxK
U2 - 10.1109/ICEEE.2009.5393456
DO - 10.1109/ICEEE.2009.5393456
M3 - Contribución a la conferencia
AN - SCOPUS:77949780965
SN - 9781424446896
T3 - 2009 6th International Conference on Electrical Engineering, Computing Science and Automatic Control, CCE 2009
BT - 2009 6th International Conference on Electrical Engineering, Computing Science and Automatic Control, CCE 2009
T2 - 2009 6th International Conference on Electrical Engineering, Computing Science and Automatic Control, CCE 2009
Y2 - 10 November 2009 through 13 November 2009
ER -