Control barrier functions for stochastic systems
Control barrier functions for stochastic systems
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DOI：
10.1016/j.automatica.2021.109688
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发表时间：
2020-03
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影响因子：
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通讯作者：
Andrew Clark
中科院分区：
文献类型：
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作者：
Andrew Clark
控制屏障功能(CBF)旨在通过在每个时间步长限制控制输入以确保安全，从而使系统状态保持在期望的安全区域内。本文提出了一种在高斯过程和测量噪声存在的随机系统中的CBF的框架。我们首先考虑了系统状态在每个时间步长已知的情况，给出了以概率1保证安全的倒易和零CBF结构。我们将我们的结果推广到高相对度系统，给出了线性动力学和仿射安全约束的一般结构和特例。然后，我们开发了用于不完全状态信息环境的CBF，在这种环境中，必须使用被高斯噪声破坏的传感器来估计状态。我们证明了当状态估计在真实状态的给定范围内时，我们所提出的CBF以概率1保证安全性，当系统是线性的或过程和测量噪声足够小时，这可以使用扩展卡尔曼滤波来实现。我们提出了将这些CBF与控制Lyapunov函数相结合的控制策略，以共同确保安全性和随机稳定性。通过对多智能体避碰场景的数值研究，验证了我们的结果。
Control Barrier Functions (CBFs) aim to ensure safety by constraining the control input at each time step so that the system state remains within a desired safe region. This paper presents a framework for CBFs in stochastic systems in the presence of Gaussian process and measurement noise. We first consider the case where the system state is known at each time step, and present reciprocal and zero CBF constructions that guarantee safety with probability 1. We extend our results to high relative degree systems and present both general constructions and the special case of linear dynamics and affine safety constraints. We then develop CBFs for incomplete state information environments, in which the state must be estimated using sensors that are corrupted by Gaussian noise. We prove that our proposed CBF ensures safety with probability 1 when the state estimate is within a given bound of the true state, which can be achieved using an Extended Kalman Filter when the system is linear or the process and measurement noise are sufficiently small. We propose control policies that combine these CBFs with Control Lyapunov Functions in order to jointly ensure safety and stochastic stability. Our results are validated via numerical study on a multi-agent collision avoidance scenario.