论文标题
部分可观测时空混沌系统的无模型预测
Fundamental Limitations of Control and Filtering in Continuous-Time Systems: An Information-Theoretic Analysis
论文作者
论文摘要
尽管已经引入了信息理论来调查和表征几十年来的控制和过滤局限性，但现有的信息理论方法是间接而繁琐的，用于分析连续时间系统的基本局限性。为了应对这一挑战，我们通过使用邓肯定理或i-MMSE关系来将信息理论分析提高到无限维度的连续功能空间。连续的时间控制和过滤系统被建模为具有或没有反馈的加性高斯通道，总信息速率被确定为控制和过滤权衡度量的度量，并直接从通道输入的估计误差进行计算。权衡度量的不平等限制是在一般环境中得出的，然后应用于捕获受线性和非线性植物的各种控制和过滤系统的基本限制。对于线性系统，我们表明总信息速率具有与某些已建立的权衡相似的属性，例如Bode-Type积分和最小估计误差。对于非线性系统，我们提供了一种直接的方法来计算Stratonovich-Kushner方程的总信息速率及其下限。
While information theory has been introduced to investigate and characterize the control and filtering limitations for a few decades, the existing information-theoretic methods are indirect and cumbersome for analyzing the fundamental limitations of continuous-time systems. To answer this challenge, we lift the information-theoretic analysis to continuous function spaces of infinite dimensions by using Duncan's theorem or the I-MMSE relationships. Continuous-time control and filtering systems are modeled as an additive Gaussian channel with or without feedback, and total information rate is identified as a control and filtering trade-off metric and directly computed from the estimation error of channel input. Inequality constraints for the trade-off metric are derived in a general setting and then applied to capture the fundamental limitations of various control and filtering systems subject to linear and nonlinear plants. For the linear systems, we show that total information rate has similar properties as some established trade-offs, e.g., Bode-type integrals and minimum estimation error. For the nonlinear systems, we provide a direct method to compute the total information rate and its lower bound by the Stratonovich-Kushner equation.
