In this study, the multiobjective H 2 /H ∞ fuzzy control design is investigated for nonlinear mean-field jump diffusion (MFSJD) systems for concurrently minimizing both H 2 and H ∞ performance. Since H 2 and H ∞ performance usually conflict with one another, the optimization problem that concurrently minimizes H 2 and H ∞ performance can be regarded as a dynamically constrained multiobjective optimization problem (MOP). Because Hamilton-Jacobi inequalities of the nonlinear MFSJD systems are difficult to derive, multiobjective H 2 /H∞ control design problems of nonlinear MFSJD system are difficult to solve. The Takagi-Sugeno fuzzy interpolation scheme and an indirect method are introduced to help transform the dynamically constrained MOP into linear matrix inequalities (LMIs) constrained MOP. Thus, one can accomplish the multiobjective H 2 /H ∞ fuzzy control design via LMI-constrained multiobjective evolutionary algorithms (MOEAs). To efficiently solve the multiobjective H 2 /H ∞ control design problem, we propose a novel LMI-constrained MOEA called fronts-squeezing. The fronts-squeezing LMI-constrained MOEA can concurrently search Pareto front from both sides of feasible and infeasible regions and narrow the search region down to increase efficiency. Finally, we present a simulation example about the multiobjective regulation of nonlinear MFSJD financial system to illustrate the design procedure and verify the proposed theories.
