受控随机非线性系统在信息约束下的遍历性：分裂的精确界
Ergodicity of Controlled Stochastic Nonlinear Systems under Information Constraints: Refined Bounds via Splitting
摘要：
研究了有限容量无噪信道上离散非线性随机系统的镇定问题。我们的重点是系统分解成一个稳定的和不稳定的组件，并考虑的稳定性概念是渐近遍历的$\mathbb{R}^N$值状态过程。我们建立了一个必要的下界信道容量的存在的编码和控制策略，使闭环系统的随机稳定。在文献中，已经确定在技术假设下，信道容量必须小于系统线性化的行列式的对数，在噪声和遍历状态测量上求平均。在本文中，我们建立了一个稳定的组成部分的系统，它足以只考虑不稳定的尺寸，提供了一个完善的一般信道容量的限制为一大类系统。结果是建立使用的概念，稳定熵，一个概念适应于不变性熵，用于研究无噪声系统的信息约束下。
英文摘要：
This paper considers the problem of stabilizing a discrete-time non-linear stochastic system over a finite capacity noiseless channel. Our focus is on systems which decompose into a stable and unstable component, and the stability notion considered is asymptotic ergodicity of the $\mathbb{R}^N$-valued state process. We establish a necessary lower bound on channel capacity for the existence of a coding and control policy which renders the closed-loop system stochastically stable. In the literature, it has been established that under technical assumptions, the channel capacity must not be smaller than the logarithm of the determinant of the system linearization, averaged over the noise and ergodic state measures. In this paper, we establish that for systems with a stable component, it suffices to consider only the unstable dimensions, providing a refinement on the general channel capacity bound for a large class of systems. The result is established using the notion of stabilization entropy, a notion adapted from invariance entropy, used in the study of noise-free systems under information constraints.
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