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Cooperative game-oriented optimal design in constraint-following control of mechanical systems

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Abstract

This paper proposes a cooperative game-oriented optimal design problem of robust control for uncertain mechanical systems. State of the concerned system is affected by (possibly fast) time-varying but bounded uncertainty. The task is to drive the system to obey a set of prescribed constraints. A \(\beta \)-measure is defined to gauge the constraint-following error; based on which, a robust control with two tunable parameters is then proposed to render the system to be uniform boundedness and uniform ultimate boundedness. For the seeking of the optimal design parameters, two cost functions, each of which is dominated by one tunable parameter, are developed, and thereout a two-player cooperative game is formulated. Finally, the optimal design problem is successfully solved: with the existence, uniqueness, and analytical expression of the Pareto-optimality. This paper is the first ever endeavor to cast both constraint following and cooperative game into control framework for uncertain mechanical systems.

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Acknowledgements

The research is supported jointly 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), the “Nanjing University of Science and Technology Independent Research Program” (No. 30920021105), and the “Jiangsu Planned Projects for Postdoctoral Research Funds” (No. 2020Z179).

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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

    Qinqin Sun, Guolai Yang & Xiuye Wang

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

    Ye-Hwa Chen

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

    Ye-Hwa Chen

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  1. Qinqin Sun
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Correspondence to Guolai Yang.

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Sun, Q., Yang, G., Wang, X. et al. Cooperative game-oriented optimal design in constraint-following control of mechanical systems. Nonlinear Dyn 101, 977–995 (2020). https://doi.org/10.1007/s11071-020-05800-6

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