为受限输入的欠驱动系统设计鲁棒安全过滤器，确保在干扰下仍能保持安全
Robust Safety Filtering for Input-Constrained Underactuated Linear Systems
- 基于零和微分博弈生成基线输入，结合干扰观测器修正
- 通过误差界构建高阶控制屏障函数，保证状态始终安全
- 适用于机器人等需精确控制的安全关键场景
针对存在未知干扰的输入受限欠驱动线性系统，本文提出一种鲁棒安全过滤框架。通过零和微分博弈获得基准 H-$\infty$ 输入，同时利用干扰观测器提供干扰估计及其瞬态误差上界。基准输入根据干扰估计进行调整，而估计值与误差上界用于定义鲁棒高阶控制屏障函数约束；只要允许输入集非空，前向不变性即可保持。对于单输入系统，点对点可行性由精确输入区间决定，区间宽度即为可行性裕度。有限时域内 H-$\infty$ 性能平衡考虑了实际输入相对于基准策略的累积偏差。在直线化两轮平衡机器人上的仿真表明，位置约束与姿态倾角约束会争夺同一有界轮扭矩输入。
原文摘要 · Abstract (English)
We present a robust safety-filtering framework for input-constrained underactuated linear systems subject to unknown disturbances. A baseline H-$\infty$ input is derived from a zero-sum differential game, while a disturbance observer supplies an estimate and a transient error bound. The baseline input is adjusted using the disturbance estimate, while the estimate and its error bound are used to define robust high-order control barrier function constraints; forward invariance holds as long as the admissible-input set remains nonempty. For scalar-input systems, pointwise feasibility is determined from an exact input interval, and the interval width defines the feasibility margin. A finite-horizon H-$\infty$ performance balance accounts for the accumulated deviation of the applied input from the baseline H-$\infty$ policy. Simulations on a linearized two-wheeled balancing robot show how position and body-pitch constraints compete for the same bounded wheel-torque input.
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