TY - JOUR
T1 - DNN-state identification of 2D distributed parameter systems
AU - Chairez, I.
AU - Fuentes, R.
AU - Poznyak, A.
AU - Poznyak, T.
AU - Escudero, M.
AU - Viana, L.
PY - 2012/2/1
Y1 - 2012/2/1
N2 - There are many examples in science and engineering which are reduced to a set of partial differential equations (PDEs) through a process of mathematical modelling. Nevertheless there exist many sources of uncertainties around the aforementioned mathematical representation. Moreover, to find exact solutions of those PDEs is not a trivial task especially if the PDE is described in two or more dimensions. 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 article, a strategy based on the differential neural network (DNN) for the non-parametric identification of a mathematical model described by a class of two-dimensional (2D) PDEs 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 behaviour of the suggested methodology, here a non-parametric modelling problem for a distributed parameter plant is analysed.
AB - There are many examples in science and engineering which are reduced to a set of partial differential equations (PDEs) through a process of mathematical modelling. Nevertheless there exist many sources of uncertainties around the aforementioned mathematical representation. Moreover, to find exact solutions of those PDEs is not a trivial task especially if the PDE is described in two or more dimensions. 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 article, a strategy based on the differential neural network (DNN) for the non-parametric identification of a mathematical model described by a class of two-dimensional (2D) PDEs 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 behaviour of the suggested methodology, here a non-parametric modelling problem for a distributed parameter plant is analysed.
KW - adaptive identification
KW - distributed parameter systems
KW - neural networks
KW - partial differential equations
KW - practical stability
UR - http://www.scopus.com/inward/record.url?scp=84857208583&partnerID=8YFLogxK
U2 - 10.1080/00207721.2010.495187
DO - 10.1080/00207721.2010.495187
M3 - Artículo
SN - 0020-7721
VL - 43
SP - 296
EP - 307
JO - International Journal of Systems Science
JF - International Journal of Systems Science
IS - 2
ER -