SCIENCE CHINA Information Sciences, Volume 62, Issue 2: 022204(2019) https://doi.org/10.1007/s11432-018-9501-9

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

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  • ReceivedApr 21, 2018
  • AcceptedJun 1, 2018
  • PublishedDec 27, 2018


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 directionsand non-parametric uncertainties. Despite this, a refined tracking objective, ratherthan a reduced one, is sought. That is, not only pre-specified arbitrary tracking accuracyis guaranteed, but also certain prescribed transient performance (e.g., arrival time andmaximum overshoot) is ensured to better meet real applications.To solve the problem, a new tracking scheme is established, crucially introducingdelicate time-varying gains to counteract the severe uncertainties and guarantee theprescribed performance. It is shown that the designed controller renders the trackingerror to forever evolve within a prescribed performance funnel, through which the desired trackingobjective is accomplished for the systems. Particularly, by subtly specifying thefunnel, global fixed-time practical tracking (i.e., that with prescribed arrival time)and semiglobal practical tracking with prescribed maximal overshoot can be achieved forthe systems. Moreover, the tracking scheme remains valid in the presence of ratherless-restrictive 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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  • Figure 1

    The evolution of system (23). The trajectory of (a) error $e$, (b) state $z$, (c) state $x_1$, (d) state $x_2$, (e) control $u$, and (f) gains $r_1$ and $r_2$.

  • Figure 2

    The evolution of system (24). The trajectory of (a) error $e$, (b) state $x_1$, (c) state $x_2$, (d) state $x_3$, (e) control $u$, (f) gain $r_1$, (g) gain $r_2$, and (h) gain $r_3$.

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