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This paper considers the global prescribed-time asymptotic tracking control problem for uncertain strict feedback nonlinear systems with time-varying parameters and an unknown control direction. A novel prescribed-time scaling function is constructed, and the frequently used basic lemma on the Nussbaum function is modified to adapt to the situation where the initial value of the control coefficient is zero. With the help of the nonlinear mapping technique, the congelation of variables method and the backstepping method, an adaptive tracking control method is presented, which exhibits several attractive features: (1) all the closed-loop signals are bounded; (2) for any initial condition, the tracking error can be confined within a prescribed zone in a prescribed time; and (3) the asymptotic convergence of the tracking error is ensured. The effectiveness of the proposed control method is demonstrated by using two simulation examples.
Shi et al. (Mon,) studied this question.