Abstract
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.
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The authors appreciate the partial financial support from the Ministry of Science and Technology of Republic of China under Grant MOST 108-2221-E-032-039-MY2 and Grant MOST 109-2222-E-032-003.
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Wu, CF., Hsu, CF. & Hwang, CK. Multiobjective H2/H∞ Control Design for Nonlinear Stochastic Chaotic Systems via a Front-Squeezing LMIs-Constrained MOEA. Int. J. Fuzzy Syst. 23, 2371–2383 (2021). https://doi.org/10.1007/s40815-021-01149-z
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DOI: https://doi.org/10.1007/s40815-021-01149-z