Abstract
In this study,in order to solve multiobjective H2/H infinity fuzzy tracking control problem in nonlinear uncertain system, a multiobjective fuzzy control design method is introduced for nonlinear uncertain systems to guarantee optimal H2 and H infinity reference tracking performance simultaneously. First, the Takagi and Sugeno (T-S) fuzzy model is used to represent the nonlinear uncertain system. Then, based on T-S fuzzy model and fuzzy controller, multiobjective H2/H infinity fuzzy tracking control problem is formulated as a multiobjective problem (MOP) to minimize the H2 tracking error and H infinity disturbance attenuation level for nonlinear fuzzy systems at the same time. Since it is not easy to solve this MOP directly, an indirect method is proposed to solve this MOP for multiobjective H2/H infinity fuzzy tracking control design, which is assuming that H2 tracking error and H infinity disturbance attenuation level have the upper bounds, and based on minimizing two upper bounds, the multiobjective problem is transformed to minimizing the multiobjective control design problem under the constraint of three linear matrix inequalities (LMIs). Then, a LMI-based multiobjective evolution algorithm (LMI-based MOEA) which used the LMI toolbox in MATLAB is developed to efficiently solve the set of Pareto optimal solutions for the MOP, from which designer can select one design according to his own preference. Further, the multiobjective H2/H infinity fuzzy control design problem based on the weighted sum method is also solved for comparison, and we also introduce the evolution algorithm in this paper.Finally, a numerical simulation is given to illustrate the design procedure and to confirm the performance of the proposed multiobjective H2/H infinity fuzzy tracking control for nonlinear uncertain system.