论文标题
差分夹杂物的相反鲁棒安全定理
A Converse Robust-Safety Theorem for Differential Inclusions
论文作者
论文摘要
本文确定了鲁棒安全性与存在差异包含物的屏障功能证书之间的等效性。更确切地说，对于鲁棒安全的差分包含，屏障函数被构造为相对于特定构造的可触及设置的影响时间函数。使用设定值和非平滑分析的技术，我们表明，尽管可能是不连续的功能，但通过验证涉及系统解决方案的条件，可以证明强大的安全性。此外，我们使用Converse Lyapunov理论文献中的平滑技术来完善这种结构，以提供平滑的屏障证书，通过仅验证仅涉及屏障功能和系统动态的状况来证明强大的安全性。与现有的Converse稳健安全定理相比，我们的结果更加笼统，因为它们允许安全区域无限制，动力学可以是一般连续的集合值地图，而解决方案则是非唯一的。
This paper establishes the equivalence between robust safety and the existence of a barrier function certificate for differential inclusions. More precisely, for a robustly-safe differential inclusion, a barrier function is constructed as the time-to-impact function with respect to a specifically-constructed reachable set. Using techniques from set-valued and nonsmooth analysis, we show that such a function, although being possibly discontinuous, certifies robust safety by verifying a condition involving the system's solutions. Furthermore, we refine this construction, using smoothing techniques from the literature of converse Lyapunov theory, to provide a smooth barrier certificate that certifies robust safety by verifying a condition involving only the barrier function and the system's dynamics. In comparison with existing converse robust-safety theorems, our results are more general as they allow the safety region to be unbounded, the dynamics to be a general continuous set-valued map, and the solutions to be non-unique.
