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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 323806, 8 pages
http://dx.doi.org/10.1155/2013/323806
Research Article

Finite Time Inverse Optimal Stabilization for Stochastic Nonlinear Systems

1College of Mathematics, Physics, and Information Engineering, Zhejiang Normal University, Jinhua 321004, China
2Laboratory of Intelligent Control and Robotics, Shanghai University of Engineering Science, Shanghai 201620, China

Received 30 April 2013; Accepted 20 June 2013

Academic Editor: Ljubisa Kocinac

Copyright © 2013 Xiushan Cai 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.

Abstract

This paper deals with finite time inverse optimal stabilization for stochastic nonlinear systems. A concept of the stochastic finite time control Lyapunov function (SFT-CLF) is presented, and a control law for finite time stabilization for the closed-loop system is obtained. Furthermore, a sufficient condition is developed for finite time inverse optimal stabilization in probability, and a control law is designed to ensure that the equilibrium of the closed-loop system is finite time inverse optimal stable. Finally, an example is given to illustrate the applications of theorems established in this paper.