Discrete Dynamics in Nature and Society
Volume 2006 (2006), Article ID 92932, 18 pages

Robust adaptive tracking for Markovian jump nonlinear systems with unknown nonlinearities

Jin Zhu, Hong-Sheng Xi, Hai-Bo Ji, and Bing Wang

Department of Automation, University of Science and Technology of China (USTC), Hefei 230027, Anhui, China

Received 12 December 2005; Accepted 27 February 2006

Copyright © 2006 Jin Zhu et al. 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.


Robust adaptive tracking problems for a class of Markovian jump parametric-strict-feed-back systems with both parametric uncertainty and unknown nonlinearity are investigated. The unknown nonlinearities considered herein lie within some “bounding functions,” which are assumed to be partially known. By using a stochastic Lyapunov method and backstepping techniques, a parameter adaptive law and a control law were obtained, which guarantee that the tracking error could be within a small neighborhood around the origin in the sense of the fourth moment. Moreover, all signals of the closed-loop system could be globally uniformly ultimately bounded.