乘积流形上带 $\mathrm{SO}(3)$ 的证书携带式分布式模型预测控制
Certificate-Carrying Distributed Model Predictive Control on Product Manifolds with $\mathrm{SO}(3)$
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中文总结 AI 辅助
本文针对同步分布式模型预测控制中相邻预测变化导致的约束违反问题，提出带硬轨迹信任区域和双层预算的证书携带式方法，证明硬约束满足与递归可行性，并在航天器编队中验证其降低保守性。
中文摘要 AI 辅助
本文研究了同步分布式模型预测控制（DMPC）中，当相邻预测在采样时刻之间发生变化时的约束认证问题。在并行局部求解之前，每个智能体通信一个移位预测和一个宣布的更新预算。硬轨迹信任区域使得该预算可强制执行，而根据移位数据包计算的边级可行性上限在不使用任何当前优化器输出的情况下保持回退可行。距离和相对姿态约束通过显式Lipschitz常数和两个预算层进行收紧：一个考虑同时邻居更新，另一个保留可检查的移位储备。我们证明了在所述标称执行和终端假设下硬成对约束满足和递归可行性，给出了由执行误差引起的额外残差，并推导了局部实用值下降界。航天器编队示例使用硬终端和成对约束、$\SO$ 上的测地相对姿态约束以及可复现的终端集检查。与固定、仅轨迹和窗口在线裕度的比较表明，所提出的预算在保持正移位可行性裕度的同时减少了保守性。
英文摘要
This paper studies constraint certification in synchronous distributed model predictive control (DMPC) when neighboring predictions change between sampling instants. Before the parallel local solves, each agent communicates a shifted prediction and an announced update budget. A hard trajectory trust region makes that budget enforceable, while an edge-wise feasibility cap computed from the shifted packets keeps the fallback feasible without using any current optimizer output. Distance and relative-attitude constraints are tightened with explicit Lipschitz constants and two budget layers: one accounts for the simultaneous neighbor update and the other retains a checkable shift reserve. We prove hard pairwise constraint satisfaction and recursive feasibility under stated nominal-execution and terminal assumptions, give the additional residual caused by execution error, and derive a local practical value-decrease bound. A spacecraft formation example uses hard terminal and pairwise constraints, a geodesic relative- attitude constraint on $\SO$, and reproducible terminal-set checks. Comparisons with fixed, trajectory-only, and windowed online margins show that the proposed budget reduces conservatism while preserving a positive shifted-feasibility margin.
发表机构
- Hubei University（湖北大学）
- Wuhan University（武汉大学）
- KTH Royal Institute of Technology（皇家理工学院）
- Northeastern University（东北大学）
机构由 AI 辅助整理，请以论文原文为准。
