Ascent Trajectory Optimization for Boost-Glide Vehicle Using Homotopy Approximation Function Sequential Convex Programming

The control capability of boost-glide vehicle models controlled by the angle of attack and the sideslip angle is weak. Such vehicles' ascent trajectory optimization exhibits characteristics of strong nonlinearity and piecewise constraints of control angles. Specifically, it faces two challenges: poor convergence performance and low computation efficiency. The algorithm's convergence is sensitive to the initial guess when traditional convex approaches based on the direct linearization method are employed. The existence of piecewise constraints of control angles increases the complexity of the problem, reducing the algorithm's computation efficiency. To effectively address these challenges, this article proposes the homotopy approximation function sequential convex programming algorithm. The high-precision approximation strategy and lossless convex relaxation are proposed to improve the convergence performance first, followed by a designed approximation function to approach the piecewise constraints of control angles. Subsequently, the originally nonconvex optimal control problem is reformulated into a series of convex optimization subproblems. Numerical simulations are conducted to verify the performance of the proposed algorithm in addressing the piecewise constraints of control angles. In addition, the optimality and real-time performance are discussed through comparative simulation examples.