Multiobjective tracking control design of T–S fuzzy systems: Fuzzy Pareto optimal approach

In this study, a multiobjective fuzzy control design method is introduced for nonlinear dynamic systems to guarantee the optimal H2H2 and H∞H∞ reference tracking performance simultaneously. First, the Takagi and Sugeno (T–S) fuzzy model is used to represent the nonlinear dynamic system. Then, based on the T–S fuzzy model, multiobjective H2/H∞H2/H∞ tracking control design problem is formulated as a multiobjective problem (MOP) to minimize the H2H2 tracking error and H∞H∞ disturbance attenuation level for the fuzzy system at the same time. Since it is not easy to solve this MOP directly, an indirect method is proposed for the multiobjective H2/H∞H2/H∞ tracking control design. Finally, in order to achieve the simultaneous optimization of the MOP, linear matrix inequality (LMI)-based multiobjective evolution algorithm (LMI-based MOEA) is developed based on non-dominating sorting scheme to efficiently search 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∞H2/H∞ fuzzy control design problem based on the weighted sum method is also solved as an alternative choice. Finally, a simulation example of a robotic system is given to illustrate the design procedure and to confirm the robust and optimal tracking performance of the proposed method.