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On time-minimal distributed control of vibrating systems governed by an abstract wave equation

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Abstract

Distributed control of vibrations governed by an abstract wave equation is studied. First it is shown that every initial state of finite energy can be transferred to a position of rest within any finite time interval by a unique control with minimumL 2-norm. If only controls with a uniformly boundedL 2-norm are admitted, the same statement is shown for sufficiently large time intervals. In this case the existence of time-minimal “null-controls” can be proved by routine arguments. In addition, time-minimal controls are characterized by the property of being least norm controls on the minimum time interval and having asL 2-norm exactly the upper bound that is prescribed. The results partly overlap with results of Fattorini.

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References

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Authors and Affiliations

  1. Fachbereich Mathematik, Technischen Hochschule Darmstadt, Schlossgartenstrasse 7, 6100, Darmstadt, West Germany

    W. Krabs

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  1. W. Krabs
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Communicated by A. V. Balakrishnan

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Krabs, W. On time-minimal distributed control of vibrating systems governed by an abstract wave equation. Appl Math Optim 13, 137–149 (1985). https://doi.org/10.1007/BF01442203

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  • DOI: https://doi.org/10.1007/BF01442203

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