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Mathematical Problems in Engineering
Volume 2013, Article ID 687317, 10 pages
http://dx.doi.org/10.1155/2013/687317
Research Article

Variance and Passivity Constrained Fuzzy Control for Nonlinear Ship Steering Systems with State Multiplicative Noises

Department of Marine Engineering, National Taiwan Ocean University, Keelung 202, Taiwan

Received 7 January 2013; Accepted 18 February 2013

Academic Editor: Chang-Hua Lien

Copyright © 2013 Wen-Jer Chang and Bo-Jyun Huang. 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 variance and passivity constrained fuzzy control problem for the nonlinear ship steering systems with state multiplicative noises is investigated. The continuous-time Takagi-Sugeno fuzzy model is used to represent the nonlinear ship steering systems with state multiplicative noises. In order to simultaneously achieve variance, passivity, and stability performances, some sufficient conditions are derived based on the Lyapunov theory. Employing the matrix transformation technique, these sufficient conditions can be expressed in terms of linear matrix inequalities. By solving the corresponding linear matrix inequality conditions, a parallel distributed compensation based fuzzy controller can be obtained to guarantee the stability of the closed-loop nonlinear ship steering systems subject to variance and passivity performance constraints. Finally, a numerical simulation example is provided to illustrate the usefulness and applicability of the proposed multiple performance constrained fuzzy control method.