Piecewise Nonsingular Practical Prescribed-Time Control for Three-Dimensional Skip-Trajectory Tracking of Hypersonic Glide Vehicles

Three-dimensional skip-reentry trajectory tracking is challenging for hypersonic glide vehicles because of strong nonlinearity, pronounced state oscillations, model parameter uncertainty, and bank-angle constraints. This paper develops a trajectory-tracking control method based on the drag-acceleration profile and piecewise nonsingular practical prescribed-time control. A three-dimensional point-mass model that accounts for the Earth’s curvature and rotation is first used with predictor–corrector guidance to generate a reference skip trajectory considering process constraints and terminal requirements. The longitudinal bank-angle magnitude and the lateral bank-angle sign are then obtained separately. Taking the cosine of the bank angle as the control input, the drag-tracking error is formulated as a second-order control-affine system. The proposed controller uses an odd cubic polynomial extension to remove the derivative singularity of low-order fractional powers near the origin, and combines a dual-power reaching law in the prescribed-time phase with a linear hyperbolic-tangent holding law after that phase. Using Dini derivatives, a cited predefined-time Lyapunov criterion, and an explicit target-entry-time estimate, it is shown that the sliding variable and the drag-tracking error enter prescribed neighborhoods within an upper time bound independent of the initial condition; positive invariance of the neighborhoods, ultimate boundedness of the second-order error, and the discretization-error correction condition are also obtained. Simulations show that the proposed method improves drag-acceleration tracking accuracy under nominal conditions and constant parameter perturbations, while keeping the closed-loop states bounded and satisfying the bank-angle constraint under random parameter perturbations and initial measurement errors. The method provides a feasible route to configurable-time tracking control for constrained skip trajectories of hypersonic glide vehicles.