Connections between minimum entropy control and mixed H2/H∞ control for time-varying systems

Marc A. Peters; Pablo A. Iglesias

doi:10.1016/0167-6911(95)00033-X

Connections between minimum entropy control and mixed H₂/H_∞ control for time-varying systems

Marc A. Peters, Pablo A. Iglesias

Whiting School of Engineering

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

3 Scopus citations

Abstract

In this paper two properties of minimum entropy control for linear time-varying systems are investigated. An entropy formulation for anti-causal systems is first considered. Minimizing the norm of an anticausal system is straightforward because of the fact that the norm of an operator is equal to the norm of its adjoint. This is not true for the entropy measure. For this reason a separate formula for the entropy of anti-causal systems is needed in order to consider dual problems that arise in optimal control theory. Secondly, we investigate the relationship between the entropy measure for time-varying systems and the H₂ and H_∞ norms. For time-invariant systems, minimum entropy control has been shown to be a good mixed H₂/H_∞ controller. In this paper we show that this is also true in the time-varying case.

Original language	English (US)
Pages (from-to)	341-347
Number of pages	7
Journal	Systems and Control Letters
Volume	26
Issue number	5
DOIs	https://doi.org/10.1016/0167-6911(95)00033-X
State	Published - Dec 27 1995

Keywords

Discrete time
Entropy
H/H
Operator norms
Time varying

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science(all)
Mechanical Engineering
Electrical and Electronic Engineering

Access to Document

10.1016/0167-6911(95)00033-X

Cite this

@article{3ccf824477f74c10ab33cc836bff0a05,

title = "Connections between minimum entropy control and mixed H2/H∞ control for time-varying systems",

abstract = "In this paper two properties of minimum entropy control for linear time-varying systems are investigated. An entropy formulation for anti-causal systems is first considered. Minimizing the norm of an anticausal system is straightforward because of the fact that the norm of an operator is equal to the norm of its adjoint. This is not true for the entropy measure. For this reason a separate formula for the entropy of anti-causal systems is needed in order to consider dual problems that arise in optimal control theory. Secondly, we investigate the relationship between the entropy measure for time-varying systems and the H2 and H∞ norms. For time-invariant systems, minimum entropy control has been shown to be a good mixed H2/H∞ controller. In this paper we show that this is also true in the time-varying case.",

keywords = "Discrete time, Entropy, H/H, Operator norms, Time varying",

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

note = "Funding Information: Minimum entropy control has been studied extensively for linear time-invariant systems, both in the continuous-and discrete-time cases. In particular, controllers satisfying a closed-loop minimum entropy condition have been shown to have considerable advantages over the standard optimal ~'~ control problem. First of all, the minimum entropy condition imposes uniqueness among the controllers which achieve an induced norm bound. Secondly, it has been shown that the entropy is an upper bound for the g2 norm of the system, and thus minimum entropy controllers provide a degree of performance sacrificed in other ~t°~ controllers. Recently, it has been shown that in some cases, these controllers * Corresponding author. E-mail: marcp@kate.ece.jhu.edu&pi @mth.eee.jhu.edu. 1 This work was supported in part by the National Science Foundation, under contract ECS-9309387.",

year = "1995",

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T1 - Connections between minimum entropy control and mixed H2/H∞ control for time-varying systems

AU - Peters, Marc A.

AU - Iglesias, Pablo A.

N1 - Funding Information: Minimum entropy control has been studied extensively for linear time-invariant systems, both in the continuous-and discrete-time cases. In particular, controllers satisfying a closed-loop minimum entropy condition have been shown to have considerable advantages over the standard optimal ~'~ control problem. First of all, the minimum entropy condition imposes uniqueness among the controllers which achieve an induced norm bound. Secondly, it has been shown that the entropy is an upper bound for the g2 norm of the system, and thus minimum entropy controllers provide a degree of performance sacrificed in other ~t°~ controllers. Recently, it has been shown that in some cases, these controllers * Corresponding author. E-mail: marcp@kate.ece.jhu.edu&pi @mth.eee.jhu.edu. 1 This work was supported in part by the National Science Foundation, under contract ECS-9309387.

PY - 1995/12/27

Y1 - 1995/12/27

N2 - In this paper two properties of minimum entropy control for linear time-varying systems are investigated. An entropy formulation for anti-causal systems is first considered. Minimizing the norm of an anticausal system is straightforward because of the fact that the norm of an operator is equal to the norm of its adjoint. This is not true for the entropy measure. For this reason a separate formula for the entropy of anti-causal systems is needed in order to consider dual problems that arise in optimal control theory. Secondly, we investigate the relationship between the entropy measure for time-varying systems and the H2 and H∞ norms. For time-invariant systems, minimum entropy control has been shown to be a good mixed H2/H∞ controller. In this paper we show that this is also true in the time-varying case.

AB - In this paper two properties of minimum entropy control for linear time-varying systems are investigated. An entropy formulation for anti-causal systems is first considered. Minimizing the norm of an anticausal system is straightforward because of the fact that the norm of an operator is equal to the norm of its adjoint. This is not true for the entropy measure. For this reason a separate formula for the entropy of anti-causal systems is needed in order to consider dual problems that arise in optimal control theory. Secondly, we investigate the relationship between the entropy measure for time-varying systems and the H2 and H∞ norms. For time-invariant systems, minimum entropy control has been shown to be a good mixed H2/H∞ controller. In this paper we show that this is also true in the time-varying case.

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