An Information-Theoretic Analysis of Discrete-Time Control and Filtering Limitations by the I-MMSE Relationships
Fundamental limitations or performance trade-offs/limits are important properties and constraints of both control and filtering systems. Among various trade-off metrics, total information rate that characterizes the sensitivity trade-offs and time-averaged performance of control and filtering systems was conventionally studied by using the differential entropy rate and Kolmogorov-Bode formula. In this paper, by extending the famous I-MMSE (mutual information -- minimum mean-square error) relationships to the discrete-time additive white Gaussian channels with and without feedback, a new paradigm is introduced to estimate and analyze total information rate as a control and filtering trade-off metric. Under this framework, we explore the trade-off properties of total information rate for a variety of the discrete-time control and filtering systems, e.g., LTI, LTV, and nonlinear, and propose an alternative approach to investigate total information rate via optimal estimation.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Neural Predictive Control to Coordinate Discrete- and Continuous-Time Models for Time-Series Analysis with Control-Theoretical Improvements
Deep sequence models have achieved notable success in time-series analysis, such as interpolation and forecasting. Recent advances move beyond discrete-time architectures like Recurrent Neural Networks (RNNs) toward cont…
Consistency analysis of refined instrumental variable methods for continuous-time system identification in closed-loop
Refined instrumental variable methods have been broadly used for identification of continuous-time systems in both open and closed-loop settings. However, the theoretical properties of these methods are still yet to be f…
Digital Controllers in Discrete and Continuous Time Domains for a Robot Arm Manipulator
This paper articulates design and performance analysis of digital controllers in discrete and continuous time domains for a single-joint robot arm manipulator. The investigated robot arm system is modeled as a single deg…
Formalizing Neuromorphic Control Systems: A General Proposal and A Rhythmic Case Study
Neuromorphic control is receiving growing attention due to the multifaceted advantages it brings over more classical control approaches, including: sparse and on-demand sensing, information transmission, and actuation; e…
Self-adaptation in non-Elitist Evolutionary Algorithms on Discrete Problems with Unknown Structure
A key challenge to make effective use of evolutionary algorithms is to choose appropriate settings for their parameters. However, the appropriate parameter setting generally depends on the structure of the optimisation p…
Evolutionary Algorithms