Discrete Dynamics in Nature and Society 
Volume 2006 (2006), Article ID 92932, 18 pages
doi:10.1155/DDNS/2006/92932

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

Abstract

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.