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Remarks on bang-bang control in Hilbert space

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Abstract

In this note, a natural definition of bang-bang control in Hilbert space is given, and some of the theory of the authors' paper (Ref. 1) is rebuilt upon it. An elliptic boundary-value problem illustrating the theory is given. In the last part of this note, the results of Ref. 1 are extended to nonlinear perturbations of linear operators and to homogeneous nonlinear operators.

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References

  1. Rogak, E. D., andKazarinoff, N. D.,Sufficient Conditions for Bang-Bang Control in Hilbert Space, Journal of Optimization Theory and Applications, Vol. 5, No. 1, 1970.

  2. Lions, J. L.,Contrôle Optimal de Systèmes Gouvernés par des Équations aux Dérivées Partielles, Dunod, Paris, 1968.

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  3. Smirnov, V. I.,A Course in Higher Mathematics, Vol. 5, Moscow, 1960.

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Author notes

  1. N. D. Kazarinoff (Professor)

    Present address: Department of Mathematics, State University of New York at Buffalo, Buffalo, New York

Authors and Affiliations

  1. Department of Mathematics, University of Victoria, Victoria, British Columbia, Canada

    E. D. Rogak (Associate Professor)

  2. Department of Mathematics, University of Michigan, Ann Arbor, Michigan

    N. D. Kazarinoff (Professor)

Authors
  1. E. D. Rogak
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  2. N. D. Kazarinoff
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Additional information

Communicated by L. Cesari

This research was supported by NRC Grant No. A-4047 and NSF Grant No. GP-7445.

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Rogak, E.D., Kazarinoff, N.D. Remarks on bang-bang control in Hilbert space. J Optim Theory Appl 10, 211–221 (1972). https://doi.org/10.1007/BF00934808

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  • DOI: https://doi.org/10.1007/BF00934808

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