AI 中文总结
本文针对航天器交会问题，提出基于参数二次规划与混合zonotope可达性分析的可验证显式MPC，突破时域限制，51步时域下控制律仅占10.5 MB、计算耗时低于300 ns，适配CubeSat飞行计算机。
AI 中文摘要
基于优化的控制器（如模型预测控制（MPC））的两个特性限制了其在航天飞行中的应用：在线计算时间会变化且可能超过采样周期，闭环行为无形式化保证。显式MPC通过计算优化问题的参数化解，用分段仿射函数的查找表替代星上优化，执行时间固定，但因区域数量随预测时域呈指数增长，仅被认为适用于小时域场景。本文基于二次规划参数化解和非凸可达性分析的最新进展，为Clohessy-Wiltshire动力学下的航天器交会控制器提供完整流程，可从计算时间和内存角度构建高效数据结构编码控制律。此外，该控制器可通过混合 zonotope（ zonotope 为 zonotope 的中文译名，此处保留原缩写）的可达性分析，离线验证并获得有保证的闭环稳定性证书。在51步预测时域下，交会控制律占用10.5 MB内存，评估时间低于300 ns，该内存占用可适配CubeSat飞行计算机ARM9级AT91RM9200，表明采用本文所述参数求解器和数据结构构建分区时，时域限制不再成立。
英文摘要
Two properties of optimization-based controllers such as model predictive control (MPC) limit their use in space flight. The online computing time varies and can exceed the sampling period, and the closed-loop behavior carries no formal guarantee. Explicit MPC, where a parametric solution of the optimization problem is computed, replaces the on-board optimization with a lookup table of piecewise-affine functions with a fixed execution time. However, it has been regarded as only applicable to small horizons, since the number of regions bounds the memory the table occupies and admits only an exponential bound in the horizon. This paper builds on recent developments in parametric solutions of quadratic programs and nonconvex reachability analysis to provide an entire pipeline for spacecraft rendezvous controllers under the Clohessy-Wiltshire dynamics. For this application, efficient data structures can be constructed to encode the control law, both from a computing time and a memory standpoint. In addition, the controller can be verified offline with a guaranteed closed-loop stability certificate by resorting to reachability analysis with hybrid zonotopes. At a 51-step horizon the rendezvous law occupies 10.5 MB and is evaluated in under 300 ns. The occupied memory would fit for instance the CubeSat flight computer ARM9-class AT91RM9200 meaning that the horizon limitation does not hold when the partition is built with the parametric solvers and data structures shown in this paper.
Comments12 pages, 5 figures, 2 tables. Submitted to IEEE Transactions on Control Systems Technology
