发表机构
University of Maryland, Baltimore County; The University of Michigan; Brigham Young University（马里兰大学巴尔的摩分校; 密歇根大学; 杨百翰大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对由凸集并集构成的非凸安全集，提出基于谱选择的凸安全滤波方法，通过选取矩阵特征向量得到凸输入约束，保证特征值几何下界，仿真验证其有效性。
AI 中文摘要
由凸集的并集构成的安全集对应的离散时间控制障碍函数条件，在控制输入层面是非凸的。对于通过矩阵非负特征值数量定义的矩阵凹函数所确定的安全集，本文证明该安全集是凸集的并集，且非凸性源于只需满足并集中至少一个成员的条件，而非所有成员。选取当前状态下矩阵函数的特征向量，可得到仅作用于确定集合成员的特征值的凸输入约束；该约束隐含了现有工作的矩阵全局条件，且能保证闭环轨迹上各相关特征值的几何下界。针对含多面体障碍物和谱面体障碍物的双积分器系统仿真，将所提滤波器与矩阵全局条件进行了对比。
英文摘要
The discrete-time control barrier function condition for a safe set that is a union of convex sets is nonconvex in the control input. For safe sets defined by a matrix concave function through the number of its nonnegative eigenvalues, this paper shows that the set is a union of convex sets, and that the nonconvexity arises because at least one member of the union must hold, not every member. Selecting eigenvectors of the matrix function at the current state yields a convex input constraint that acts only on the eigenvalues determining membership in the set. This constraint is implied by the matrix-wide condition of prior work, and it guarantees a geometric lower bound on each of those eigenvalues along closed-loop trajectories. A double-integrator simulation with a polytope obstacle and a spectrahedron obstacle compares the proposed filter with the matrix-wide condition.
Comments7 pages, 3 figures, submitted to the ACC 2027
