论文标题
无界噪声的网络控制的渐近最佳两部分固定速率编码方案
An Asymptotically Optimal Two-Part Fixed-Rate Coding Scheme for Networked Control with Unbounded Noise
论文作者
论文摘要
众所周知，在固定速率信息约束下，自适应量化器可用于稳定在$ \ mathbb {r}^n $上由无界噪声驱动的$ \ mathbb {r}^n $上的开循环 - 不稳定系统。这些自适应方案可以设计到它们的速度几乎是最佳的速率，并且所得系统将在具有不变的概率度量或善良的概率以及第二时刻的界限的情况下保持稳定。尽管已经研究了编码器的结构结果和信息理论界限，但尚未解决这种适应性固定速率量化器的性能。在本文中，我们提出了一个分为两部分的自适应（固定速率）编码方案，该方案在噪声过程中的轻度矩条件下，在噪声过程中实现了与经典最佳（即完全观察到的设置）的第二次计算。与先前的工作一样，第一部分会导致终结性（通过正哈里斯复发），而第二部分确保了状态第二瞬间以高速率收敛到经典的最佳最佳。这些结果是使用复杂的分析来建立的，该分析使用随机时间依赖性Lyapunov随机漂移标准作为核心工具。
It is known that under fixed-rate information constraints, adaptive quantizers can be used to stabilize an open-loop-unstable linear system on $\mathbb{R}^n$ driven by unbounded noise. These adaptive schemes can be designed so that they have near-optimal rate, and the resulting system will be stable in the sense of having an invariant probability measure, or ergodicity, as well as boundedness of the state second moment. Although structural results and information theoretic bounds of encoders have been studied, the performance of such adaptive fixed-rate quantizers beyond stabilization has not been addressed. In this paper, we propose a two-part adaptive (fixed-rate) coding scheme that achieves state second moment convergence to the classical optimum (i.e., for the fully observed setting) under mild moment conditions on the noise process. The first part, as in prior work, leads to ergodicity (via positive Harris recurrence) and the second part ensures that the state second moment converges to the classical optimum at high rates. These results are established using an intricate analysis which uses random-time state-dependent Lyapunov stochastic drift criteria as a core tool.
