  In this paper, a fixed-time safe control problem is investigated for an
uncertain high-order nonlinear pure-feedback system with state constraints. A
new nonlinear transformation function is firstly proposed to handle both the
constrained and unconstrained cases in a unified way. Further, a radial basis
function neural network is constructed to approximate the unknown dynamics in
the system and a fixed-time dynamic surface control (FDSC) technique is
developed to facilitate the fixed-time control design for the uncertain
high-order pure-feedback system. Combined with the proposed unified
transformation function and the FDSC technique, an adaptive fixed-time control
strategy is proposed to guarantee the fixed-time tracking. The proposed
fixed-time control strategy can guarantee uniform control structure when
addressing both constrained and unconstrained situations. Numerical examples
are presented to demonstrate the proposed fixed-time tracking control strategy.
