通过屏障调节辅助变量在受扰高相对阶系统中合成无限时间最优控制的安全性
Synthesizing Safety in Infinite-Horizon Optimal Control for Disturbed High-Relative-Degree Systems via Barrier-Regulating Auxiliary Variables
AI总结：
本文通过引入屏障调节辅助变量，将受扰高相对阶系统的约束问题转化为扩展状态空间上的无约束问题，结合自适应对齐条件的切向激励和H∞框架，提升安全与性能的平衡，实现扰动下的安全运行。
摘要：
最优稳定安全关键非线性系统需要平衡长期性能和严格安全约束。现有基于二次规划的控制屏障函数（CBF）安全过滤器是点式的，当保障动作与名义最优控制冲突时可能表现出短视行为和局部陷阱。本文通过将屏障-李雅普诺夫函数（BLF）基于的保障动作嵌入系统动力学，并引入屏障调节辅助变量，将原约束问题重新表述为扩展状态空间上的无约束问题。为缓解局部陷阱，引入自适应对齐条件的切向激励，其激活程度自适应调节由名义控制器与保障控制器之间的方向对齐程度决定，并将其作为适定的L2扰动纳入H∞框架中。对于受扰的高相对阶系统，进一步通过递归高阶安全集构造和屏障补偿项获得高阶BLF，并提出对抗性扰动抑制问题，通过安全探索增强的在线批评学习近似求解。仿真显示减少局部陷阱，改善安全-性能权衡，并在扰动下实现安全运行。
英文摘要：
Optimal stabilization of safety-critical nonlinear systems requires balancing long-term performance and strict safety constraints. Existing quadratic-programming-based control barrier function (CBF) safety filters are point-wise and may exhibit myopic behavior and local trapping when the safeguarding action conflicts with the nominal optimal control. This paper develops a safety-aware infinite-horizon optimal control framework by embedding a barrier-Lyapunov function (BLF)-based safeguarding action into the system dynamics and introducing a barrier-regulating auxiliary variable, thereby reformulating the original constrained problem as an unconstrained one on an extended state space. To mitigate local trapping, we introduce an adaptive alignment-conditioned tangential excitation orthogonal to the safety direction, with activation adaptively modulated by the degree of directional alignment between the nominal and safeguarding controllers, and incorporate it as an admissible $\mathcal{L}2$ disturbance in an $H\infty$ formulation. For high-relative-degree systems under disturbances, we further augment the recursive high-order safe-set construction with barrier compensation terms to obtain a high-order BLF and formulate an adversarial disturbance attenuation problem, which is approximately solved via safe-exploration-enhanced online critic learning. Simulations demonstrate reduced local trapping, improved safety--performance trade-offs, and safe operation under disturbances.
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