适用于椭圆轨道航天器交会的依赖预测时域的Tube MPC，带条件鲁棒约束满足
Horizon-Dependent Tube MPC for Spacecraft Rendezvous on Elliptical Orbits with Conditional Robust Constraint Satisfaction
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中文总结 AI 辅助
本文针对椭圆轨道航天器交会问题，开发了依赖预测时域的Tube MPC，可在相当燃料成本下大幅降低走廊违规次数，且在超出设计包络时能明确保证的丧失。
中文摘要 AI 辅助
椭圆轨道上的航天器交会需在导航噪声、未建模扰动及推进剂质量不确定性导致的推力误差下保持安全走廊。本文针对Yamanaka-Ankersen线性时变动力学开发了基于Tube的模型预测控制器，将约束收紧的Tube方法从圆轨道扩展至椭圆轨道。一种依赖预测时域的逐元素误差界沿预测窗口传播实际闭环矩阵，因此早期预测步骤可保留恒定宽度Tube会放弃的几乎完整走廊。乘性到加性的转换将质量和推力不确定性纳入同一收紧递推，且Perron-Frobenius谱半径条件提供了可计算的收敛证书，带有显式输入-状态稳定性增益。在火星样本返回轨道的配对蒙特卡洛试验中，该Tube控制器与名义预测基准相比，在相当的燃料成本下将平均走廊违规次数减少了一个数量级以上。在远超假设扰动预算的扁率扰动下的非线性真值模型测试中，走廊未被违反；当超出设计包络时，收紧问题变得不可行，控制器切换至饱和线性 fallback，使保证的丧失明确而非隐性。该构造仅需逐元素算术运算和开源二次规划求解器。
英文摘要
Spacecraft rendezvous on elliptical orbits must hold a safety corridor under navigation noise, unmodelled perturbations, and thrust errors driven by propellant mass uncertainty. This paper develops a tube-based model predictive controller for the Yamanaka-Ankersen linear time-varying dynamics, carrying constraint-tightening tube methods from circular to elliptical orbits. A horizon-dependent, element-wise error bound propagates the actual closed-loop matrices along the prediction window, so early prediction steps keep nearly the full corridor that a constant-width tube would surrender. A multiplicative-to-additive conversion folds mass and thrust uncertainty into the same tightening recursion, and a Perron-Frobenius spectral-radius condition supplies a computable certificate that the tightening converges, with an explicit input-to-state stability gain. In a paired Monte Carlo campaign on a Mars sample-return orbit, the tube controller cuts mean corridor violations by more than an order of magnitude against a nominal predictive baseline at comparable fuel cost. A nonlinear truth-model test with oblateness perturbations well beyond the assumed disturbance budget leaves the corridor unviolated, and when the design envelope is exceeded the tightened problem becomes infeasible and the controller reverts to a saturated linear fallback, making the loss of guarantee explicit rather than silent. The construction requires only element-wise arithmetic and an open-source quadratic-programming solver.
