While information-theoretic methods have been introduced to investigate the fundamental control and filtering limitations for a few decades, currently, there is no direct method or trade-off metric to analyze the limitations of continuous- and discrete-time problems within a unified framework. To answer this challenge, we lift the traditional information-theoretic methods to infinite-dimensional spaces and formulate various control and filtering systems uniformly as noisy communication channels. Channel capacity and total information rate are studied from the perspective of general control and filtering trade-off, and computed from the estimation errors of channel inputs. Fundamental constraints on the trade-off metrics are derived and used to capture the limitations of continuous-time control and filtering systems. For the control and filtering systems in the linear case, the general trade-offs serve as the performance limits related to the characteristics of plant models. For the systems with nonlinear plants, we compute the general trade-offs and their lower bounds by resorting to the Stratonovich-Kushner equation.

翻译：虽然几十年来采用了信息理论方法来调查基本控制和过滤限制,但目前还没有直接的方法或权衡尺度来分析统一框架内连续和单独时间问题的限制。为了应对这一挑战,我们将传统的信息理论方法提升到无限空间,并制订各种控制与过滤系统,统一作为吵闹的通信渠道;从一般控制和过滤取舍的角度研究频道能力和总体信息率,并根据频道投入的估计错误进行计算;取舍标准的基本限制是用来并用来捕捉连续时间控制和过滤系统的局限性;对于线性控制与过滤系统来说,一般的权衡是同植物模型特征有关的性能限制;对于非线性工厂的系统,我们通过采用Stratonovich-Kushner方程式来计算一般交易及其下限。