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A FAS approach for stabilization of generalized chained forms: part 1. Discontinuous control laws

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Abstract

In this paper, a type of general nonholonomic systems is proposed, which contains both the Brockett’s two example systems, and their extended n-dimensional chained forms, as special cases. For the stabilization of such systems, a stabilizing controller is proposed based on the fully actuated system (FAS) approach, which is discontinuous at the origin but time-invariant when the open-loop system is time-invariant, and drives the feasible trajectories of the system to the origin exponentially. Furthermore, the proposed FAS approach is also extended to the sub-normal system case and the time-delay system case.

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Acknowledgements

This work has been partially supported by Shenzhen Key Laboratory of Control Theory and Intelligent Systems (Grant No. ZDSYS20220330161800001), Major Program of National Natural Science Foundation of China (Grant Nos. 61690210, 61690212), National Natural Science Foundation of China (Grant No. 61333003), and Science Center Program of the National Natural Science Foundation of China (Grant No. 62188101). The author is grateful to his Ph.D. students, Weizhen LIU, Guangtai TIAN, Qin ZHAO, etc., for helping him with reference selection and proofreading. His thanks also go to Prof. Zhongping JIANG, Drs. Wei SUN, Xiang XU, and Tao LIU for helpful discussions and comments. He particularly thanks Dr. Zhongcai ZHANG for helping work out the simulation results. Finally, the author thanks the anonymous reviewers for the helpful suggestions.

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  1. Center for Control Science and Technology, Southern University of Science and Technology, Shenzhen, 518055, China

    Guang-Ren Duan

  2. Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, 150001, China

    Guang-Ren Duan

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  1. Guang-Ren Duan
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Correspondence to Guang-Ren Duan.

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Duan, GR. A FAS approach for stabilization of generalized chained forms: part 1. Discontinuous control laws. Sci. China Inf. Sci. 67, 122201 (2024). https://doi.org/10.1007/s11432-022-3730-8

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