Multiobjective H2/H∞ Control Design for Nonlinear Stochastic Chaotic Systems via a Front-Squeezing LMIs-Constrained MOEA

This study proposes the multiobjective $$H_{2}/H_{{\infty }}$$ fuzzy control design for a nonlinear stochastic chaotic system via concurrently optimizing $$H_{2}$$ and $$H_{{\infty }}$$ performance indices in a Pareto optimal sense. Using the Takagi–Sugeno fuzzy model to approximate the nonlinear stochastic chaotic system, the multiobjective $$H_{2}/H_{{\infty}}$$ fuzzy control design problem can be transformed into a linear matrix inequalities (LMIs)-constrained multiobjective optimization problem (an LMIs-constrained MOP). By the help of the LMIs-constrained multiobjective evolution algorithm (LMIs-constrained MOEA), one can obtain the Pareto optimal controller. However, the existing LMIs-constrained MOEA usually couples with a heavy computational load. This study proposes the front-squeezing LMIs-constrained MOEA to resolve such a computational cost problem. Finally, a simulation example is presented to verify the effectiveness of the proposed theories.