Observation of nonlinear systems via finite capacity channels: Constructive data rate limits
Observation of nonlinear systems via finite capacity channels: Constructive data rate limits
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DOI：
10.1016/j.automatica.2016.04.005
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发表时间：
2016-08-01
期刊：
影响因子：
6.4
通讯作者：
Pogrornsky, Alexander
中科院分区：
文献类型：
--
作者：
Matveev, Alexey;Pogrornsky, Alexander
本文讨论了通过有限容量的通信信道观测非线性和确定性的，虽然可能是混沌的离散时间系统。我们介绍了几个最小的数据速率限制与各种类型的可观测性，并提供新的易于处理的分析技术，其上限和下限的估计。而较低的估计是通过以下的李雅普诺夫线性化方法的线路，建议的上估计技术是沿着第二李雅普诺夫方法的线路。作为一个说明性的例子，所提出的结果的潜力被证明为系统，它描述了一个球的正弦振动台上垂直弹跳。对于这个系统，我们提供了一个分析计算的封闭形式的表达的阈值，分离的信道数据速率，可靠的观察是不可能的，分别。另一个例子是著名的Henon系统。所提供的足够的数据速率界限是伴随着一个建设性的观察员，只要信道容量适合这个界限。(C)2016爱思唯尔有限公司版权所有。
The paper deals with observation of nonlinear and deterministic, though maybe chaotic, discrete-time systems via finite capacity communication channels. We introduce several minimum data-rate limits associated with various types of observability, and offer new tractable analytical techniques for their both upper and lower estimation. Whereas the lower estimate is obtained by following the lines of the Lyapunov's linearization method, the proposed upper estimation technique is along the lines of the second Lyapunov approach. As an illustrative example, the potential of the presented results is demonstrated for the system which describes a ball vertically bouncing on a sinusoidally vibrating table. For this system, we provide an analytical computation of a closed-form expression for the threshold that separates the channel data rates for which reliable observation is and is not possible, respectively. Another illustration is concerned with the celebrated Henon system. The offered sufficient data rate bound is accompanied with a constructive observer that works whenever the channel capacity fits this bound. (C) 2016 Elsevier Ltd. All rights reserved.