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On the Pontryagin maximum principle for constant-time linear control systems in Banach spaces

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Abstract

We give some dual characterizations (i.e., in terms of certain suprema) of linear systems satisfying the Pontryagin maximum principle. We give several applications, among which a solution of a problem raised by Rolewicz.

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References

  1. Rolewicz, S.,Linear Systems in Banach Spaces, Calculus of Variations and Control Theory, Edited by D. L. Russell, Academic Press, New York, New York, 1976.

    Google Scholar 

  2. Rolewicz, S.,On General Theory of Linear Systems, Beiträge zur Analysis, Vol. 8, pp. 119–127, 1976.

    Google Scholar 

  3. Rolewicz, S.,Analiza Funkcjonalna i Teoria Sterowania, PWN, Warszawa, Poland, 1974.

    Google Scholar 

  4. Singer, I.,On a Problem of Moments of S. Rolewicz, Studia Mathematica, Vol. 48, pp. 95–98, 1973.

    Google Scholar 

  5. Dixmier, J.,Sur un Théorème de Banach, Duke Mathematical Journal, Vol. 15, pp. 1057–1071, 1948.

    Google Scholar 

  6. Dunford, N., andSchwartz, J.,Linear Operators, Part I: General Theory, John Wiley and Sons (Interscience Publishers), New York, New York, 1958.

    Google Scholar 

  7. Bishop, E., andPhelps, R. R.,A Proof that Every Banach Space is Subreflexive, Bulletin of the American Mathematical Society, Vol. 67, pp. 97–98, 1961.

    Google Scholar 

  8. Rogosinski, W. W.,On Finite Systems of Linear Equations with an Infinity of Unknowns, Mathematische Zeitscrift, Vol. 63, pp. 97–108, 1955.

    Google Scholar 

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Communicated by L. D. Berkovitz

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Singer, I. On the Pontryagin maximum principle for constant-time linear control systems in Banach spaces. J Optim Theory Appl 27, 315–321 (1979). https://doi.org/10.1007/BF00933235

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