Observation of nonlinear systems via finite capacity channels: Part II: Restoration entropy and its estimates

Alexey S. Matveev; Alexander Yu Pogromsky

doi:10.1016/j.automatica.2019.01.019

Observation of nonlinear systems via finite capacity channels: Part II: Restoration entropy and its estimates

Alexey S. Matveev (Corresponding author)
, Alexander Yu Pogromsky

Dynamics and Control

Research output: Contribution to journal › Article › Academic › peer-review

24 Citations (Scopus)

169 Downloads (Pure)

Abstract

The paper deals with the state estimation problem for nonlinear dynamical systems via communication channels with limited data rate. We introduce several minimum data-rate limits associated with various types of observability. A notion of the restoration entropy (RE) is also introduced and its relevance to the problem is outlined by a corresponding Data Rate Theorem. Theoretical lower and upper estimates for the RE are proposed in the spirit of the first and second Lyapunov methods, respectively. For three classic chaotic multi-dimensional systems, it is demonstrated that the lower and upper estimates for the RE coincide for one of them and are nearly the same for the others.

Original language	English
Pages (from-to)	189-199
Number of pages	11
Journal	Automatica
Volume	103
DOIs	https://doi.org/10.1016/j.automatica.2019.01.019
Publication status	Published - 1 May 2019

Keywords

Entropy
Lyapunov function
Nonlinear systems
Observability
Reliable state estimation

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10.1016/j.automatica.2019.01.019

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abstract = "The paper deals with the state estimation problem for nonlinear dynamical systems via communication channels with limited data rate. We introduce several minimum data-rate limits associated with various types of observability. A notion of the restoration entropy (RE) is also introduced and its relevance to the problem is outlined by a corresponding Data Rate Theorem. Theoretical lower and upper estimates for the RE are proposed in the spirit of the first and second Lyapunov methods, respectively. For three classic chaotic multi-dimensional systems, it is demonstrated that the lower and upper estimates for the RE coincide for one of them and are nearly the same for the others.",

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AU - Pogromsky, Alexander Yu

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Y1 - 2019/5/1

N2 - The paper deals with the state estimation problem for nonlinear dynamical systems via communication channels with limited data rate. We introduce several minimum data-rate limits associated with various types of observability. A notion of the restoration entropy (RE) is also introduced and its relevance to the problem is outlined by a corresponding Data Rate Theorem. Theoretical lower and upper estimates for the RE are proposed in the spirit of the first and second Lyapunov methods, respectively. For three classic chaotic multi-dimensional systems, it is demonstrated that the lower and upper estimates for the RE coincide for one of them and are nearly the same for the others.

AB - The paper deals with the state estimation problem for nonlinear dynamical systems via communication channels with limited data rate. We introduce several minimum data-rate limits associated with various types of observability. A notion of the restoration entropy (RE) is also introduced and its relevance to the problem is outlined by a corresponding Data Rate Theorem. Theoretical lower and upper estimates for the RE are proposed in the spirit of the first and second Lyapunov methods, respectively. For three classic chaotic multi-dimensional systems, it is demonstrated that the lower and upper estimates for the RE coincide for one of them and are nearly the same for the others.

KW - Entropy

KW - Lyapunov function

KW - Nonlinear systems

KW - Observability

KW - Reliable state estimation

UR - https://www.scopus.com/pages/publications/85060164325

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DO - 10.1016/j.automatica.2019.01.019

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SN - 0005-1098

VL - 103

SP - 189

EP - 199

JO - Automatica

JF - Automatica

ER -

Observation of nonlinear systems via finite capacity channels: Part II: Restoration entropy and its estimates

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Keywords

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