基于平方和可达性的备份控制障碍函数综合
Backup Control Barrier Function Synthesis using Sum-of-Squares Reachability
AI总结：
该研究针对输入受限非线性系统，提出基于有限时间域平方和反向可达性的备份控制障碍函数综合方法，生成更优备份配对以扩大安全集，提升bCBF框架的安全认证能力。
AI中文摘要：
备份控制障碍函数（bCBF）通过预先认证的备份集和控制器，对输入受限的非线性系统实施安全保障，但其性能高度依赖于这一指定的配对。本文提出一种构造性方法，通过有限时间域平方和（SOS）反向可达性来综合更具保守性的备份配对。从初始备份集出发，我们计算出经SOS认证的有限时间域反向可达集和控制器，这些集合与控制器需满足安全和输入约束，同时将轨迹引导至原始备份集。随后，我们给出条件，使该认证集合成为分段备份控制器的有效备份集。最终得到的备份配对被集成到bCBF框架中，以认证更大的安全集。
英文摘要：
Backup control barrier functions (bCBFs) enforce safety for input-constrained nonlinear systems using a pre-certified backup set and controller, but their performance depends strongly on this prescribed pair. This letter develops a constructive method for synthesizing a less conservative backup pair via finite horizon sum-of-squares (SOS) backward reachability. Starting from an initial backup set, we compute an SOS-certified finite horizon backward reachable set and controller that satisfy safety and input constraints while steering trajectories to the original backup set. We then provide conditions under which this certified set becomes a valid backup set for a piecewise backup controller. The resulting backup pair is integrated into the bCBF framework to certify larger safe sets.
