考虑强气动力的可重复使用火箭动力着陆的浓缩PIPG序列凸优化
Condensed PIPG Sequential Convex Optimization for Reusable-Rocket Powered Landing with Strong Aerodynamics
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中文总结 AI 辅助
针对强气动力下可重复使用火箭动力着陆问题，提出带精确降维架构的浓缩PIPG序列凸优化方法，经验证可获紧最优解，辅以多种加速器提升性能。
中文摘要 AI 辅助
在强气动力作用下的可重复使用火箭动力着陆问题，通过非线性速度框架动力学耦合了变质量、自由终端时间以及有界气动力控制。本文提出了一种浓缩比例-积分投影梯度（PIPG）序列凸方法，其主要贡献在于精确降维的内部架构。由于该问题仅包含6个终端硬等式且无状态路径约束，从31节点凸子问题中消除了217个节点状态变量和210个梯形动力学等式，剩余101个原始变量和6个终端等式。行正交预处理、固定大小的矩阵-向量乘积以及逐节点的上境图圆投影，进而生成定制化的PIPG内核。通过逐步释放参考平方角与上境图变量A之间的阻力敏感度，结合凸紧项，维持了与角度相关的轴向力的物理一致性。逐点哈密顿论证表明，完全释放的极限子问题存在满足A=α²+β²的紧最优解。确定性退火、两阶段内部精度以及失败时拒绝的三重外推，是次要的外循环加速器。
英文摘要
Reusable-rocket powered landing under strong aerodynamics couples variable mass, free final time, and bounded aerodynamic controls through nonlinear velocity-frame dynamics. This paper develops a condensed proportional--integral projected-gradient (PIPG) sequential-convex method whose principal contribution is an exact reduced-space inner architecture. Because the problem contains only six terminal hard equalities and no state path constraints, 217 nodal-state variables and 210 trapezoidal dynamics equalities are eliminated from the 31-node convex subproblem, leaving 101 primal variables and six terminal equalities. Row-orthogonal preconditioning, fixed-size matrix--vector products, and nodewise circular-epigraph projections then yield a customized PIPG kernel. Physical consistency of the angle-dependent axial force is maintained by gradually releasing drag sensitivity between the reference squared angle and an epigraph variable $A$, together with a convex tightness term. A pointwise Hamiltonian argument shows that the fully released limiting subproblem admits a tight optimum satisfying $A=α^2+β^2$. Deterministic annealing, two-stage inner accuracy, and a rejected-on-failure threefold extrapolation are secondary outer-loop accelerators.
