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Practical Finite-Time Fuzzy Control for Hamiltonian Systems via Adaptive Event-Triggered Approach

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Abstract

This paper is to present our new results on practical finite-time fuzzy control scheme for a class of Hamiltonian systems by an adaptive event-triggered approach. An unknown function of the system is approximated by an adaptive fuzzy system. According to a semi-global practical finite-time stability criterion, a novel adaptive fuzzy finite-time controller is presented. In the interest of saving resources, an event-triggered approach is developed where the controller is updated under the respective triggering conditions. Based on the special structure of Hamiltonian systems and Lyapunov theory, a sufficient condition is obtained so that the states of original systems converge to a small neighborhood containing the origin in a finite time. Meanwhile, with the proposed controller, there exists a positive lower bound for the interexecution time, and the Zeno phenomenon is avoided. The design processes of the proposed controller, adaptive law and event-triggered conditions are also proved by a circuit system simulation example.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant 61703232, and in part by the Natural Science Foundation of Shandong Province under Grant ZR2017MF068 and ZR2017QF013.

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  1. Institute of Automation, Qufu Normal University, Qufu, Shandong, People’s Republic of China

    Weiwei Sun & Xinyu Lv

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  1. Weiwei Sun
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Correspondence to Weiwei Sun.

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Sun, W., Lv, X. Practical Finite-Time Fuzzy Control for Hamiltonian Systems via Adaptive Event-Triggered Approach. Int. J. Fuzzy Syst. 22, 35–45 (2020). https://doi.org/10.1007/s40815-019-00773-0

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