Global practical tracking with prescribed transient performance for inherently nonlinear systems with extremely severe uncertainties

  • Fengzhong Li
  • Yungang LiuEmail author
Research Paper


This paper considers the global practical tracking for a class of uncertain nonlinear systems. Remarkably, the systems under investigation admit rather inherent nonlinearities, and especially allow arguably the most severe uncertainties: unknown control directions and non-parametric uncertainties. Despite this, a refined tracking objective, rather than a reduced one, is sought. That is, not only pre-specified arbitrary tracking accuracy is guaranteed, but also certain prescribed transient performance (e.g., arrival time and maximum overshoot) is ensured to better meet real applications. To solve the problem, a new tracking scheme is established, crucially introducing delicate time-varying gains to counteract the severe uncertainties and guarantee the prescribed performance. It is shown that the designed controller renders the tracking error to forever evolve within a prescribed performance funnel, through which the desired tracking objective is accomplished for the systems. Particularly, by subtly specifying the funnel, global fixed-time practical tracking (i.e., that with prescribed arrival time) and semiglobal practical tracking with prescribed maximal overshoot can be achieved for the systems. Moreover, the tracking scheme remains valid in the presence of rather less-restrictive unmodeled dynamics.


nonlinear systems practical tracking prescribed transient performance unknown control directions non-parametric uncertainties unmodeled dynamics 



This work was supported by National Natural Science Foundation of China (Grant Nos. 61325016, 61703237, 61873146), Natural Science Foundation of Shandong Province (Grant No. ZR2017BF034), and China Postdoctoral Science Foundation Funded Project (Grant Nos. 2017M610424, 2018T110690).


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Copyright information

© Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Control Science and EngineeringShandong UniversityJinanChina

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