Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 325859, 16 pages
Research Article

GA-Based Fuzzy Sliding Mode Controller for Nonlinear Systems

P. C. Chen,1 C. W. Chen,2 and W. L. Chiang1

1Department of Civil Engineering, National Central University, Chung-li 32011, Taiwan
2Department of Logistics Management, College of Management, Shu-Te University, Kaohsiung 82445, Taiwan

Received 20 February 2008; Revised 4 June 2008; Accepted 8 August 2008

Academic Editor: Paulo Gonçalves

Copyright © 2008 P. C. Chen 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.


Generally, the greatest difficulty encountered when designing a fuzzy sliding mode controller (FSMC) or an adaptive fuzzy sliding mode controller (AFSMC) capable of rapidly and efficiently controlling complex and nonlinear systems is how to select the most appropriate initial values for the parameter vector. In this paper, we describe a method of stability analysis for a GA-based reference adaptive fuzzy sliding model controller capable of handling these types of problems for a nonlinear system. First, we approximate and describe an uncertain and nonlinear plant for the tracking of a reference trajectory via a fuzzy model incorporating fuzzy logic control rules. Next, the initial values of the consequent parameter vector are decided via a genetic algorithm. After this, an adaptive fuzzy sliding model controller, designed to simultaneously stabilize and control the system, is derived. The stability of the nonlinear system is ensured by the derivation of the stability criterion based upon Lyapunov's direct method. Finally, an example, a numerical simulation, is provided to demonstrate the control methodology.