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Optimal Design of Adaptive Robust Control for Bounded Constraint-Following Error in Fuzzy Mechanical Systems

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Abstract

This paper proposes an optimal indirect approach for asymmetric bounds in constraint-following in mechanical systems with (possibly fast) time-varying fuzzy uncertainty. The uncertainty is described with fuzzy set theory. We aim at optimal controller to drive the constraint-following error of the concerned fuzzy system to lie within a desired (possibly asymmetric) bound all the time and get to be sufficiently small eventually. For deterministic performance, we transform the fuzzy original system into a constructed fuzzy system, for which a deterministic (not the usual if-then rules-based) adaptive robust control is designed for uniform boundedness and uniform ultimate boundedness. For optimal performance, a performance index is proposed based on the fuzzy information, by minimizing which an optimal control gain design problem is formulated and solved. When the constructed fuzzy system is uniform boundedness and uniform ultimate boundedness, the constraint-following error of the original fuzzy system is proved to be bounded. As a result, the control design can render out deterministic performance and minimum performance index.

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Acknowledgements

The research is supported by the “Natural Science Foundation of China” (No. 51805263), the “Provincial Natural Science Foundation of Jiangsu” (No. BK20180474), the “Fundamental Research Funds for the Central Universities” (No. 309181B8811), and the “Graduate Student Scientific Research Innovation Projects of Jiangsu Province” (No. \(\hbox {SJKY19}\_0289\)). The research of Ye-Hwa Chen was supported by the Fundamental Research Funds for the Central Universities (No. 300102258305).

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Authors and Affiliations

  1. The School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, 210094, Jiangsu, People’s Republic of China

    Xiuye Wang, Qinqin Sun & Guolai Yang

  2. The Key Laboratory of Road Construction Technology and Equipment of MOE, Chang’an University, Xi’an, 710064, Shanxi, People’s Republic of China

    Ye-Hwa Chen

  3. The George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia, 30332, USA

    Ye-Hwa Chen

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  1. Xiuye Wang
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  2. Qinqin Sun
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  3. Guolai Yang
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  4. Ye-Hwa Chen
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Correspondence to Qinqin Sun.

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Wang, X., Sun, Q., Yang, G. et al. Optimal Design of Adaptive Robust Control for Bounded Constraint-Following Error in Fuzzy Mechanical Systems. Int. J. Fuzzy Syst. 22, 970–984 (2020). https://doi.org/10.1007/s40815-019-00792-x

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