Deterministic learning of nonlinear dynamical systems

Cong Wang, David Hill, Guanrong Chen

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

29 Citations (Scopus)


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.

Original languageEnglish
Title of host publicationIEEE International Symposium on Intelligent Control - Proceedings
PublisherIEEE, Institute of Electrical and Electronics Engineers
Number of pages6
Publication statusPublished - 2003
Externally publishedYes
EventIEEE International Symposium on Intelligent Control 2003 - Houston, United States of America
Duration: 5 Oct 20038 Oct 2003 (Proceedings)


ConferenceIEEE International Symposium on Intelligent Control 2003
Country/TerritoryUnited States of America
Internet address

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