An Information-Theoretic Analysis of Discrete-Time Control and Filtering Limitations by the I-MMSE Relationships
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866908268626968576 |
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| author | Wan, Neng Li, Dapeng Hovakimyan, Naira Voulgaris, Petros G. |
| author_facet | Wan, Neng Li, Dapeng Hovakimyan, Naira Voulgaris, Petros G. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_09274 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An Information-Theoretic Analysis of Discrete-Time Control and Filtering Limitations by the I-MMSE Relationships Wan, Neng Li, Dapeng Hovakimyan, Naira Voulgaris, Petros G. Systems and Control Information Theory Optimization and Control 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. |
| title | An Information-Theoretic Analysis of Discrete-Time Control and Filtering Limitations by the I-MMSE Relationships |
| topic | Systems and Control Information Theory Optimization and Control |
| url | https://arxiv.org/abs/2304.09274 |