Adaptive Prescribed-Time Stabilization of Uncertain Nonlinear Systems with Unknown Control Directions

This paper studies the adaptive prescribed-time control problem for a class of nonlinear systems with unknown time-varying control coefficients. Existing methods about unknown control direction problem can only achieve the asymptotic stability based on Barbalat's lemma. Different from these results, we present a new theorem in conjunction with Nussbaum functions to achieve the prescribed-time stability. Meanwhile, the conservative condition of Nussbaum parameters is relaxed under time-varying control coefficients, which increases the applicability of control algorithm. Based on this theorem, an adaptive prescribed-time control method for high-order nonlinear systems is proposed, which guarantees that the state variables of system converge to zero in a prescribed time rather than infinity. Finally, theoretical analysis and numerical simulations are provided to validate the effectiveness of the proposed method.