Corrections and extensions of "optimal control of linear systems with almost periodic input" by G. Da Prato and A. Ichikawa

Birgit Jacob, Mikael Larsen, Hans Zwart

Research output: Contribution to journalArticleAcademicpeer-review

9 Citations (Scopus)
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Abstract

G. Da Prato and A. Ichikawa consider in their 1987 paper the optimal control problem for linear systems with almost periodic inputs. In order to get their results they use the space $B_{ap}^2(H)$, the completion of the space of almost periodic functions in the quadratic mean. They used that $B_{ap}^2(U)$-inputs give almost periodic outputs. By means of a scalar example we show that this does not hold in general. We prove that one of their main results still holds. Furthermore, we extend this result to all forcing terms in $B_{ap}^2(H)$ and show that if the forcing term is almost periodic, then the optimal control is almost periodic as well.
Original languageEnglish
Pages (from-to)1473-1480
Number of pages8
JournalSIAM journal on control and optimization
Volume36
Issue number4
DOIs
Publication statusPublished - 1998

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Almost Periodic
Linear systems
Optimal Control
Linear Systems
Forcing Term
Almost Periodic Functions
Completion
Optimal Control Problem
Scalar
Output

Keywords

  • Almost periodic functions
  • Optimal control problem
  • Tracking problem

Cite this

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title = "Corrections and extensions of {"}optimal control of linear systems with almost periodic input{"} by G. Da Prato and A. Ichikawa",
abstract = "G. Da Prato and A. Ichikawa consider in their 1987 paper the optimal control problem for linear systems with almost periodic inputs. In order to get their results they use the space $B_{ap}^2(H)$, the completion of the space of almost periodic functions in the quadratic mean. They used that $B_{ap}^2(U)$-inputs give almost periodic outputs. By means of a scalar example we show that this does not hold in general. We prove that one of their main results still holds. Furthermore, we extend this result to all forcing terms in $B_{ap}^2(H)$ and show that if the forcing term is almost periodic, then the optimal control is almost periodic as well.",
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author = "Birgit Jacob and Mikael Larsen and Hans Zwart",
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issn = "0363-0129",
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Corrections and extensions of "optimal control of linear systems with almost periodic input" by G. Da Prato and A. Ichikawa. / Jacob, Birgit; Larsen, Mikael; Zwart, Hans.

In: SIAM journal on control and optimization, Vol. 36, No. 4, 1998, p. 1473-1480.

Research output: Contribution to journalArticleAcademicpeer-review

TY - JOUR

T1 - Corrections and extensions of "optimal control of linear systems with almost periodic input" by G. Da Prato and A. Ichikawa

AU - Jacob, Birgit

AU - Larsen, Mikael

AU - Zwart, Hans

PY - 1998

Y1 - 1998

N2 - G. Da Prato and A. Ichikawa consider in their 1987 paper the optimal control problem for linear systems with almost periodic inputs. In order to get their results they use the space $B_{ap}^2(H)$, the completion of the space of almost periodic functions in the quadratic mean. They used that $B_{ap}^2(U)$-inputs give almost periodic outputs. By means of a scalar example we show that this does not hold in general. We prove that one of their main results still holds. Furthermore, we extend this result to all forcing terms in $B_{ap}^2(H)$ and show that if the forcing term is almost periodic, then the optimal control is almost periodic as well.

AB - G. Da Prato and A. Ichikawa consider in their 1987 paper the optimal control problem for linear systems with almost periodic inputs. In order to get their results they use the space $B_{ap}^2(H)$, the completion of the space of almost periodic functions in the quadratic mean. They used that $B_{ap}^2(U)$-inputs give almost periodic outputs. By means of a scalar example we show that this does not hold in general. We prove that one of their main results still holds. Furthermore, we extend this result to all forcing terms in $B_{ap}^2(H)$ and show that if the forcing term is almost periodic, then the optimal control is almost periodic as well.

KW - Almost periodic functions

KW - Optimal control problem

KW - Tracking problem

U2 - 10.1137/S0363012996304614

DO - 10.1137/S0363012996304614

M3 - Article

VL - 36

SP - 1473

EP - 1480

JO - SIAM journal on control and optimization

JF - SIAM journal on control and optimization

SN - 0363-0129

IS - 4

ER -