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On the Relation between Topological Entropy and Restoration Entropy
1Fakultät für Informatik und Mathematik, Universität Passau, Innstraße 33, 94032 Passau, Germany.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
Restoration entropy is generally higher than topological entropy for most dynamical systems. This finding suggests that robust state estimation policies require greater data transmission rates compared to non-robust ones.
Area of Science:
- Dynamical systems theory
- Information theory
- Control theory
Background:
- State estimation under communication constraints is crucial for many applications.
- Dynamical entropy measures, including topological entropy and restoration entropy, are key metrics in this field.
- Understanding the relationship between these entropy measures is vital for designing efficient estimation policies.
Purpose of the Study:
- To present a theorem comparing restoration entropy and topological entropy for dynamical systems.
- To investigate the implications of this comparison for the design of robust state estimation policies.
- To establish a theoretical link between system dynamics, communication constraints, and estimation robustness.
Main Methods:
- Development of a novel theorem based on sophisticated tools from the theory of smooth dynamical systems.
- Mathematical analysis to demonstrate the strict inequality between restoration entropy and topological entropy.
- Theoretical framework for analyzing data transmission rates in robust versus non-robust estimation.
Main Results:
- A theorem proving that restoration entropy strictly exceeds topological entropy for most dynamical systems.
- Demonstration that robust estimation policies necessitate a higher data transmission rate than non-robust ones.
- Quantification of the difference in information requirements based on entropy measures.
Conclusions:
- The study establishes a fundamental relationship between different notions of dynamical entropy.
- Findings imply that enhanced robustness in state estimation comes at the cost of increased communication bandwidth.
- The results provide theoretical guidance for optimizing data transmission rates in communication-constrained estimation problems.
Keywords:
Anosov diffeomorphismsSRB measuresrestoration entropystate estimation under communication constraintstopological entropyMore Related Videos
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