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Backstepping control for output-constrained nonlinear systems based on nonlinear mapping

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Abstract

In this paper, nonlinear mapping (NM)-based backstepping control design is presented for a class of strict-feedback nonlinear systems with output constraint. By mapping output value set onto the set of all real numbers, the constrained system is transformed into a new strict-feedback unconstrained system to employ the traditional backstepping control while simultaneously preventing the constraint from being violated. It is proved that the original system has the similar convergence and bounded properties with the new one. Besides the nominal case where full knowledge of the plant is available, we also tackle scenarios wherein parametric uncertainties are present. Furthermore, the comparison with barrier Lyapunov function-based algorithm reveals the advantages of NM algorithm. The closed-loop system is guaranteed to be stable in the sense that all signals involved remain bounded, and the tracking error converges to zero asymptotically. Simulation studies illustrate the performance of the proposed control.

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Acknowledgments

This work was supported by the key scientific and technological research of Henan Science and Technology Division (112102210126) and the Foundation of Henan Educational Committee (13A520017, 2011B120001).

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Authors and Affiliations

  1. School of Computer and Information Engineering, Anyang Normal University, Anyang, 455002, Henan, China

    Tao Guo

  2. School of Automotive Engineering, Henan Vocational and Technical College of Communications, Zhengzhou, 450005, Henan, China

    Xiaowei Wu

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  1. Tao Guo
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  2. Xiaowei Wu
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Correspondence to Tao Guo.

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Guo, T., Wu, X. Backstepping control for output-constrained nonlinear systems based on nonlinear mapping. Neural Comput & Applic 25, 1665–1674 (2014). https://doi.org/10.1007/s00521-014-1650-9

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  • DOI: https://doi.org/10.1007/s00521-014-1650-9

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