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Multiobjective Optimization Control for Uncertain Nonlinear Stochastic System with State-Delay

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Abstract

This paper is concerned with the problem of multiobjective \(H_{2}/H_{\infty }\) control for uncertain nonlinear stochastic systems with state-delay. The main aim is to get the multiobjective \(H_{2}/H_{\infty }\) optimization performance in Pareto optimal sense. By applying T–S fuzzy approach, the multiobjective \(H_{2}/H_{\infty }\) fuzzy control problem is transformed into linear matrix inequality (LMI)-constrained multiobjective problem (MOP). In addition, we efficiently solve Pareto optimal solutions for the MOP of fuzzy control design problem by employing LMI-based multiobjective evolution algorithm. The designers can freely select multiobjective \(H_{2}/H_{\infty }\) control scheme according to their own preferences. Finally, a financial system example is given to illustrate the effectiveness and usefulness of the proposed method.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grants 61573177, 61773191 and the Natural Science Foundation of Shandong Province for Outstanding Young Talents in Provincial Universities under Grant ZR2016JL025.

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Authors and Affiliations

  1. School of Mathematics Science, Liaocheng University, Liaocheng, 252000, People’s Republic of China

    Yang Yang, Jianli Zhao, Jianwei Xia & Guangming Zhuang

  2. College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, 266590, People’s Republic of China

    Weihai Zhang

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  1. Yang Yang
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  2. Jianli Zhao
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  3. Jianwei Xia
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  4. Guangming Zhuang
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Correspondence to Jianwei Xia.

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Yang, Y., Zhao, J., Xia, J. et al. Multiobjective Optimization Control for Uncertain Nonlinear Stochastic System with State-Delay. Int. J. Fuzzy Syst. 21, 72–83 (2019). https://doi.org/10.1007/s40815-018-0541-0

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