无界噪声网络控制中的渐近最优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
摘要：
已知在固定速率信息约束下，自适应量化器可用于镇定由无界噪声驱动的$\mathbb{R}^n$上的开环不稳定线性系。这些自适应方案可以被设计成使得它们具有接近最优的速率，并且所得到的系统在具有不变的概率测度或遍历性以及状态二阶矩的有界性的意义上是稳定的。虽然编码器的结构结果和信息理论界已被研究，这种自适应固定速率量化器的性能超出稳定还没有得到解决。在本文中，我们提出了一个两部分自适应（固定速率）编码方案，实现状态二阶矩收敛到经典的最佳（即，对于充分观察的设置）在噪声过程的温和力矩条件下。第一部分，在以前的工作中，导致遍历性（通过积极的哈里斯复发）和第二部分，确保状态二阶矩收敛到经典的最佳高利率。这些结果是建立使用一个复杂的分析，使用随机时间依赖状态的李雅普诺夫随机漂移准则作为核心工具。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
