Sequential convex optimization for hypersonic vehicle trajectory planning with selective virtual control and bidirectional progressive envelope relaxation

Trajectory optimization for boost–glide hypersonic vehicles is challenging because of strongly nonlinear dynamics, non-convex control constraints, and the artificial infeasibility that may arise during sequential convex programming (SCP). This paper proposes an enhanced SCP framework that integrates selective virtual control and bidirectional progressive envelope relaxation (BPER). The selective virtual-control strategy introduces relaxation only in weakly controllable state channels identified through controllability analysis, thereby reducing unnecessary artificial freedom in the convexified dynamics. For the transformed aerodynamic-control equality, BPER combines an affine lower-envelope constraint with a convex quadratic upper-envelope constraint. The resulting relaxation variables provide a two-sided certificate for the residual of the original control equality. Numerical experiments over a 15-target boost–glide test set show that the proposed framework improves convergence robustness and recovers the transformed-control equality within the prescribed tolerance. Comparisons with a traditional SCP formulation and a pseudo-spectral benchmark demonstrate the improved robustness of the proposed method over the tested target envelope. A supplementary case verifies simultaneous node-wise enforcement of representative dynamic-pressure, convective-heating, and aerodynamic-load-factor limits.