Entropy formula for nonlinear systems

Pablo A. Iglesias; Marc A. Peters

doi:10.1016/S0016-0032(00)00055-7

Entropy formula for nonlinear systems

Pablo A. Iglesias, Marc A. Peters

Whiting School of Engineering

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

5 Scopus citations

Abstract

Minimum entropy control theory provides a powerful means of trading off the advantages of optimal H₂ and H_∞ controllers. In this paper, a framework for the nonlinear minimum entropy control problem is suggested, based on the nonlinear spectral factorization problem. It is also shown that, for a large class of H_∞ suboptimal controllers, the central controller minimizes the closed-loop entropy. The techniques used are similar to the time-domain notion of the entropy that was introduced by the authors for time-varying systems.

Original language	English (US)
Pages (from-to)	859-874
Number of pages	16
Journal	Journal of the Franklin Institute
Volume	337
Issue number	7
DOIs	https://doi.org/10.1016/S0016-0032(00)00055-7
State	Published - Nov 2000

ASJC Scopus subject areas

Control and Systems Engineering
Signal Processing
Computer Networks and Communications
Applied Mathematics

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title = "Entropy formula for nonlinear systems",

abstract = "Minimum entropy control theory provides a powerful means of trading off the advantages of optimal H2 and H∞ controllers. In this paper, a framework for the nonlinear minimum entropy control problem is suggested, based on the nonlinear spectral factorization problem. It is also shown that, for a large class of H∞ suboptimal controllers, the central controller minimizes the closed-loop entropy. The techniques used are similar to the time-domain notion of the entropy that was introduced by the authors for time-varying systems.",

author = "Iglesias, {Pablo A.} and Peters, {Marc A.}",

note = "Funding Information: This work was supported in part by the National Science Foundation, under grants ECS-9309387 and ECS-9800057. We are also grateful to the an anonymous reviewer for the comments on the viscosity solution of the Hamilton–Jacobi equation that appear in the Remark after Lemma 2 and for the remark following Lemma 10 . An earlier version of this paper was presented at the 31st Conference on Information Sciences and Systems, Baltimore, MD. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.",

year = "2000",

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AU - Iglesias, Pablo A.

AU - Peters, Marc A.

N1 - Funding Information: This work was supported in part by the National Science Foundation, under grants ECS-9309387 and ECS-9800057. We are also grateful to the an anonymous reviewer for the comments on the viscosity solution of the Hamilton–Jacobi equation that appear in the Remark after Lemma 2 and for the remark following Lemma 10 . An earlier version of this paper was presented at the 31st Conference on Information Sciences and Systems, Baltimore, MD. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.

PY - 2000/11

Y1 - 2000/11

N2 - Minimum entropy control theory provides a powerful means of trading off the advantages of optimal H2 and H∞ controllers. In this paper, a framework for the nonlinear minimum entropy control problem is suggested, based on the nonlinear spectral factorization problem. It is also shown that, for a large class of H∞ suboptimal controllers, the central controller minimizes the closed-loop entropy. The techniques used are similar to the time-domain notion of the entropy that was introduced by the authors for time-varying systems.

AB - Minimum entropy control theory provides a powerful means of trading off the advantages of optimal H2 and H∞ controllers. In this paper, a framework for the nonlinear minimum entropy control problem is suggested, based on the nonlinear spectral factorization problem. It is also shown that, for a large class of H∞ suboptimal controllers, the central controller minimizes the closed-loop entropy. The techniques used are similar to the time-domain notion of the entropy that was introduced by the authors for time-varying systems.

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Entropy formula for nonlinear systems

Abstract

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