论文标题
用于验证和合成控制屏障功能的半代数框架
A Semi-Algebraic Framework for Verification and Synthesis of Control Barrier Functions
论文作者
论文摘要
安全是医学，运输，制造和其他应用中控制系统的关键特性，可以定义为确保预定义的安全集的积极不变性。本文研究了验证半代数集的正不变性以及可以通过基于控制屏障功能（CBF）控制的阳性不变性的综合集的正不变性的问题。我们方法的关键是通过从实际代数几何形状的potitivstellensatz绘制正不变性的映射条件。基于这些条件，我们提出了一个框架，用于验证基于CBF的控制的安全性，包括单个CBF，高阶CBF，Multi-CBF和具有三角动力学和驱动约束的系统。 在综合领域，我们提出了用于构建CBF的算法，即交替发育方法和局部CBF方法。我们通过对四型无人机和电源转换器测试系统的案例研究评估我们的方法。
Safety is a critical property for control systems in medicine, transportation, manufacturing, and other applications, and can be defined as ensuring positive invariance of a predefined safe set. This paper investigates the problems of verifying positive invariance of a semi-algebraic set as well as synthesizing sets that can be made positive invariant through Control Barrier Function (CBF)-based control. The key to our approach consists of mapping conditions for positive invariance to sum-of-squares constraints via the Positivstellensatz from real algebraic geometry. Based on these conditions, we propose a framework for verifying safety of CBF-based control including single CBFs, high-order CBFs, multi-CBFs, and systems with trigonometric dynamics and actuation constraints. In the area of synthesis, we propose algorithms for constructing CBFs, namely, an alternating-descent approach and a local CBF approach. We evaluate our approach through case studies on quadrotor UAV and power converter test systems.
