Time-optimal control of multivariable systems near the origin

G.J. Olsder

Research output: Contribution to journalArticleAcademic

3 Citations (Scopus)
64 Downloads (Pure)

Abstract

This article deals with bang-bang solutions of linear time-optimal control problems. Linear multivariable systems are considered which have one or more control components. It is shown in which way the control components act together to make the system achieve the ultimate aim (namely, the origin in the state space) as quickly as possible. The theory only applies to initial positions sufficiently near the origin. Criteria are given which give the number of switches per control component. Asymptotic dependences of the switching times and the final time on the distance of the initial position from the origin are established. The theory provides a numerical procedure to calculate the time-optimal control. These calculations are very simple. Basic to the proof of these results is a generalized implicit function theorem due to Artin (Ref. 1).
Original languageUndefined
Pages (from-to)497-517
JournalJournal of optimization theory and applications
Volume16
Issue number5-6
DOIs
Publication statusPublished - 1975

Keywords

  • IR-85578

Cite this

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abstract = "This article deals with bang-bang solutions of linear time-optimal control problems. Linear multivariable systems are considered which have one or more control components. It is shown in which way the control components act together to make the system achieve the ultimate aim (namely, the origin in the state space) as quickly as possible. The theory only applies to initial positions sufficiently near the origin. Criteria are given which give the number of switches per control component. Asymptotic dependences of the switching times and the final time on the distance of the initial position from the origin are established. The theory provides a numerical procedure to calculate the time-optimal control. These calculations are very simple. Basic to the proof of these results is a generalized implicit function theorem due to Artin (Ref. 1).",
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Time-optimal control of multivariable systems near the origin. / Olsder, G.J.

In: Journal of optimization theory and applications, Vol. 16, No. 5-6, 1975, p. 497-517.

Research output: Contribution to journalArticleAcademic

TY - JOUR

T1 - Time-optimal control of multivariable systems near the origin

AU - Olsder, G.J.

PY - 1975

Y1 - 1975

N2 - This article deals with bang-bang solutions of linear time-optimal control problems. Linear multivariable systems are considered which have one or more control components. It is shown in which way the control components act together to make the system achieve the ultimate aim (namely, the origin in the state space) as quickly as possible. The theory only applies to initial positions sufficiently near the origin. Criteria are given which give the number of switches per control component. Asymptotic dependences of the switching times and the final time on the distance of the initial position from the origin are established. The theory provides a numerical procedure to calculate the time-optimal control. These calculations are very simple. Basic to the proof of these results is a generalized implicit function theorem due to Artin (Ref. 1).

AB - This article deals with bang-bang solutions of linear time-optimal control problems. Linear multivariable systems are considered which have one or more control components. It is shown in which way the control components act together to make the system achieve the ultimate aim (namely, the origin in the state space) as quickly as possible. The theory only applies to initial positions sufficiently near the origin. Criteria are given which give the number of switches per control component. Asymptotic dependences of the switching times and the final time on the distance of the initial position from the origin are established. The theory provides a numerical procedure to calculate the time-optimal control. These calculations are very simple. Basic to the proof of these results is a generalized implicit function theorem due to Artin (Ref. 1).

KW - IR-85578

U2 - 10.1007/BF00933855

DO - 10.1007/BF00933855

M3 - Article

VL - 16

SP - 497

EP - 517

JO - Journal of optimization theory and applications

JF - Journal of optimization theory and applications

SN - 0022-3239

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