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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 529251, 9 pages
http://dx.doi.org/10.1155/2012/529251
Research Article

Adaptive Control and Synchronization of the Shallow Water Model

Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290, Thailand

Received 6 July 2011; Revised 24 September 2011; Accepted 26 September 2011

Academic Editor: Carlo Cattani

Copyright © 2012 P. Sangapate. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The shallow water model is one of the important models in dynamical systems. This paper investigates the adaptive chaos control and synchronization of the shallow water model. First, adaptive control laws are designed to stabilize the shallow water model. Then adaptive control laws are derived to chaos synchronization of the shallow water model. The sufficient conditions for the adaptive control and synchronization have been analyzed theoretically, and the results are proved using a Barbalat's Lemma.