Title :
Deterministic learning of nonlinear dynamical systems
Author :
Wang, Cong ; Hill, David J. ; Chen, Guanrong
Author_Institution :
Dept. of Electron. Eng., City Univ. of Hong Kong, China
Abstract :
In this paper, we present an approach for neural networks (NN) based identification of unknown nonlinear dynamical systems undergoing periodic or periodic-like (recurrent) motions. Among various types of NN architectures, we use a dynamical version of the localized RBF neural network, which is shown to be particularly suitable for identification in a dynamical framework. With the associated properties of localized RBF networks, especially the one concerning the persistent excitation (PE) condition for periodic trajectories, the proposed approach achieves sufficiently accurate identification of system dynamics in a local region along the experienced system trajectory. In particular, for neurons whose centers are close to the trajectories, the neural weights converge to a small neighborhood of a set of optimal values; while for other neurons with centers far away from the trajectories, the neural weights are not updated and are almost unchanged. The proposed approach implements a sort of "deterministic learning" in the sense that deterministic features of nonlinear dynamical systems are learned not by algorithms from statistical principles, but in a dynamical, deterministic manner, utilizing results from adaptive systems theory. The nature of this deterministic learning is closely related to the exponentially stability of a class of nonlinear adaptive systems. Simulation studies are included to demonstrate the effectiveness of the proposed approach.
Keywords :
adaptive systems; asymptotic stability; identification; learning (artificial intelligence); nonlinear dynamical systems; radial basis function networks; NN architecture; PE condition; adaptive systems theory; deterministic features; deterministic learning; exponential stability; localized RBF neural network; neural weights; nonlinear adaptive systems; nonlinear dynamical systems; periodic motions; persistent excitation; radial basis function neural network; recurrent motions;
Conference_Titel :
Intelligent Control. 2003 IEEE International Symposium on
Conference_Location :
Houston, TX, USA
Print_ISBN :
0-7803-7891-1
DOI :
10.1109/ISIC.2003.1253919