论文标题
在高层次度约束下进行安全验证的小生命定理
Small-Gain Theorem for Safety Verification under High-Relative-Degree Constraints
论文作者
论文摘要
本文开发了一种用于安全性分析和验证具有高质量安全性限制的互连系统的小型技术。在此技术中，输入到州安全（ISSF）用于表征子系统的安全性如何受外部输入的影响，并且使用高相对程度的ISSF助推器功能（ISSF-BFS）用于捕获子系统的安全性。通过协调转换，建立了ISSF-BFS与现有的高率高（或高阶）屏障功能之间的关系，以简化ISSF分析。借助高层次的ISSF-BFS，提出了一个小生殖定理以进行安全验证。结果表明，在小增益条件下，i）ISSF子系统的互连仍然是ISSF； ii）总体互连系统是相对于组成安全集的输入到州稳定的（ISS）。提出的小生殖定理的有效性在两个倒置的摆在两个弹簧上连接的倒置摆的分散控制上说明了。
This paper develops a small-gain technique for the safety analysis and verification of interconnected systems with high-relative-degree safety constraints. In this technique, input-to-state safety (ISSf) is used to characterize how the safety of a subsystem is influenced by the external input, and ISSf-barrier functions (ISSf-BFs) with high relative degree are employed to capture the safety of subsystems. With a coordination transform, the relationship between ISSf-BFs and the existing high-relative-degree (or high-order) barrier functions is established in order to simplify the ISSf analysis. With the help of high-relative-degree ISSf-BFs, a small-gain theorem is proposed for safety verification. It is shown that, under the small-gain condition, i) the interconnection of ISSf subsystems is still ISSf; and ii) the overall interconnected system is input-to-state stable (ISS) with respect to the compositional safe set. The effectiveness of the proposed small-gain theorem is illustrated on the output-constrained decentralized control of two inverted pendulums connected by a spring mounted on two carts.
