AI 中文总结
本文针对部分可观非线性控制系统，扩展CBVF框架，结合共形预测得到误差界，推导概率安全保证，提出QP型在线安全滤波器，在避障案例中验证了框架的有效性。
AI 中文摘要
本文研究部分可观非线性控制系统的安全分析与控制器综合问题。我们将结合哈密顿-雅可比可达性与控制障碍函数的控制障碍-值函数（CBVF）框架，扩展至无法获取完整状态信息、仅能基于估计状态进行控制的场景。给定一个估计器，我们对估计误差应用共形预测，得到用户选定错误覆盖率水平下的误差界。我们将该误差界纳入估计器空间的安全分析，定义部分可观系统的CBVF型安全证书。随后推导真实系统状态的有限时间域概率安全保证。最后，针对控制与扰动仿射的系统，我们提出一种基于QP的在线安全滤波器，其解可实时强制执行CBVF安全条件以应对有界扰动。所提框架在部分可观避障案例研究中得到验证。
英文摘要
This paper studies safety analysis and controller synthesis for partially observable nonlinear control systems. We extend the control barrier--value function (CBVF) framework, which combines Hamilton--Jacobi reachability and control barrier functions, to settings where full state information is not available and control is based on an estimated state. Given an estimator, we apply conformal prediction to the estimation error and obtain an error bound at a user-chosen miscoverage level. We incorporate this bound into the estimator-space safety analysis and define a CBVF-based safety certificate for partially observable systems. We then derive a finite-horizon probabilistic safety guarantee for the true system state. Finally, we propose a QP-based online safety filter for systems affine in the control and disturbance, whose solution enforces the CBVF safety condition in real time against bounded disturbance. The proposed framework is illustrated on a partially observable obstacle-avoidance case study.
