ABSTRACT
In this chapter, a multi-objective fuzzy control design method is introduced for nonlinear dynamic systems to guarantee the optimal H2 and H∞ reference tracking performance simultaneously. First, the Takagi and Sugeno fuzzy model is used to represent the nonlinear dynamic system. Then, based on the T-S fuzzy model, the multi-objective H2 /H∞ tacking control design problem is formulated as a multi-objective problem to minimize the H2 tacking error and 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 multi-objective H2 /H∞ tracking control design. Finally, in order to achieve simultaneous optimization of the MOP, a reverse-order linear matrix inequality–based multi-objective evolution algorithm is developed based on a nondominating sorting scheme to efficiently search the set of Pareto optimal solutions for the MOP, from which the designer can select a design according to their preference. Further, the multi-objective 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.
