标题： 具有多个控制障碍函数的约束非线性系统的兼容性 显示英文标题

标题： Compatibility of Multiple Control Barrier Functions for Constrained Nonlinear Systems

摘要： 控制屏障函数（CBFs）是用于非线性系统约束控制的强大工具；然而，文献中的大多数结果集中在仅受单个CBF约束的系统上，这使得合成可证明安全的控制器来处理多个状态约束变得具有挑战性。 本文提出了一种框架，用于在系统向量值输出受到箱形约束的情况下，对非线性系统进行约束控制，该框架使用多个CBFs。 我们的结果表明，当输出具有向量相对阶时，编码这些箱形约束的CBF约束是相容的， resulting optimization-based controller 是局部Lipschitz连续的，并且可以表达为显式形式。 还提供了额外的结果，以描述在存在安全约束的情况下名义跟踪目标的退化情况。 给出了平面四旋翼机的仿真结果，以展示所提出框架的有效性。 显示英文摘要

摘要： Control barrier functions (CBFs) are a powerful tool for the constrained control of nonlinear systems; however, the majority of results in the literature focus on systems subject to a single CBF constraint, making it challenging to synthesize provably safe controllers that handle multiple state constraints. This paper presents a framework for constrained control of nonlinear systems subject to box constraints on the systems' vector-valued outputs using multiple CBFs. Our results illustrate that when the output has a vector relative degree, the CBF constraints encoding these box constraints are compatible, and the resulting optimization-based controller is locally Lipschitz continuous and admits a closed-form expression. Additional results are presented to characterize the degradation of nominal tracking objectives in the presence of safety constraints. Simulations of a planar quadrotor are presented to demonstrate the efficacy of the proposed framework.