解决延迟系统状态约束难题，无需辅助函数即可保证安全
Predictive Control Barrier Functions for Discrete-Time Linear Systems with Unmodeled Delays
- 通过扩展预测时域构造等效一阶系统，直接生成安全函数
- 在延迟双积分器和无人飞行器上验证，安全集与函数超水平集完全一致
- 适合需严格安全约束的实时控制系统，如无人机、自动驾驶
本文提出一种针对具有未知相对阶（由输入延迟或未建模动态引起）的离散时间系统的预测控制屏障函数（PCBF）框架，用于强制执行状态约束。现有离散时间CBF方法在相对阶大于1时通常需构建辅助屏障函数，这增加了实现复杂度并可能导致保守的安全集。所提PCBF框架通过扩展预测时域，为一个相对阶为1的关联系统构造屏障函数，使得该屏障函数的超水平集恰好等于安全集，从而简化了约束处理，无需额外辅助函数。方法在带输入延迟的离散时间双积分器系统和带有位置约束的无人直升机系统上进行了验证，结果表明其有效性和优越性。
原文摘要 · Abstract (English)
This paper introduces a predictive control barrier function (PCBF) framework for enforcing state constraints in discrete-time systems with unknown relative degree, which can be caused by input delays or unmodeled input dynamics. Existing discrete-time CBF formulations typically require the construction of auxiliary barrier functions when the relative degree is greater than one, which complicates implementation and may yield conservative safe sets. The proposed PCBF framework addresses this challenge by extending the prediction horizon to construct a CBF for an associated system with relative degree one. As a result, the superlevel set of the PCBF coincides with the safe set, simplifying constraint enforcement and eliminating the need for auxiliary functions. The effectiveness of the proposed method is demonstrated on a discrete-time double integrator with input delay and a bicopter system with position constraints.
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