Multiobjective H2/H∞ Control Design of the Nonlinear Mean-Field Stochastic Jump-Diffusion Systems via Fuzzy Approach

In this study, the multiobjective H-2/H-infinity fuzzy control design is investigated for nonlinear mean-field jump diffusion (MFSJD) systems for concurrently minimizing both H-2 and H-infinity performance. Since H-2 and H-infinity performance usually conflict with one another, the optimization problem that concurrently minimizes H-2 and H-infinity 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-infinity 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-infinity fuzzy control design via LMI-constrained multiobjective evolutionary algorithms (MOEAs). To efficiently solve the multiobjective H-2/H-infinity 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.