对抗可观察性与最优控制中的性能权衡
Adversarial Observability and Performance Trade-offs in Optimal Control
AI总结：
本文提出了一种在最优控制中最小化对抗传感器可观察性的反馈控制器，通过半正定规划实现性能与可观察性之间的权衡。
摘要：
我们开发了一个反馈控制器，该控制器在满足严格闭环性能约束的前提下，最小化线性系统一组对抗性传感器的可观察性。我们通过可观察性格拉姆矩阵的迹及其逆来量化对抗性传感器的有效性，捕捉系统的平均可观察性和最不可观察的状态方向。我们推导了这些指标在性能约束下的理论下界，表征了可观察性降低的基本限制作为性能权衡函数。最后，我们显示在性能约束下优化格拉姆矩阵的迹可以表示为一次半正定规划，而通过顺序半正定规划解决其逆的优化问题。飞机的模拟展示了所提出方案如何产生在降低对抗可观察性的同时具有近最优性能的控制器。
英文摘要：
We develop a feedback controller that minimizes the observability of a set of adversarial sensors of a linear system, while adhering to strict closed-loop performance constraints. We quantify the effectiveness of adversarial sensors using the trace of their observability Gramian and its inverse, capturing both average observability and the least observable state directions of the system. We derive theoretical lower bounds on these metrics under performance constraints, characterizing the fundamental limits of observability reduction as a function of the performance trade-off. Finally, we show that the performance-constrained optimization of the Gramian's trace can be formulated as a one-shot semidefinite program, while we address the optimization of its inverse through sequential semidefinite programming. Simulations on an aircraft show how the proposed scheme yields controllers that deteriorate adversarial observability while having near-optimal performance.
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