论文标题
LQR控制与稀疏的对抗性干扰
LQR Control with Sparse Adversarial Disturbances
论文作者
论文摘要
网络物理系统和事件触发的控制的最新发展导致人们对稀疏干扰对动态过程的影响引起了人们的兴趣。我们通过分析三个不同的政策来研究稀疏干扰下的线性二次调节器（LQR）控制：盲目的在线政策，骚动感知政策和最佳的离线政策。在假设控制器具有有关其位置及时的概率模型的信息的假设，我们可以得出最佳干扰感知策略的二维复发结构。在温和的条件下，我们表明，如果干扰的数量在时光范围内增加，则骚动感知政策会融合到盲目的在线政策。最后，我们在盲目的在线政策和最佳离线政策之间提供了有限的途径，事实证明，这在干扰数量和大小上是二次的。当面对意外的稀疏扰动时，这提供了标准LQR控制器的次级临时性的有用表征。
Recent developments in cyber-physical systems and event-triggered control have led to an increased interest in the impact of sparse disturbances on dynamical processes. We study Linear Quadratic Regulator (LQR) control under sparse disturbances by analyzing three distinct policies: the blind online policy, the disturbance-aware policy, and the optimal offline policy. We derive the two-dimensional recurrence structure of the optimal disturbance-aware policy, under the assumption that the controller has information about future disturbance values with only a probabilistic model of their locations in time. Under mild conditions, we show that the disturbance-aware policy converges to the blind online policy if the number of disturbances grows sublinearly in the time horizon. Finally, we provide a finite-horizon regret bound between the blind online policy and optimal offline policy, which is proven to be quadratic in the number of disturbances and in their magnitude. This provides a useful characterization of the suboptimality of a standard LQR controller when confronted with unexpected sparse perturbations.
