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On optimal control and reachable sets in a Banach space

  • Optimal Control: Partial Differential Equations
  • Conference paper
  • First Online:
Optimization Techniques

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 22))

Abstract

The problem considered in this paper is to formulate some theorems concerning infinite-dimensional control systems in Banach spaces. The theory of orientor fields developed in early sixties by T. Ważewski turned to be the suitable basis for such considerations. Passing to a Banach space we had to reject very important but rather strong assumption concerning compactivness of the orientor set. For the proofs and some auxiliary theorems we refer the reader to [8]. Let us observe that the equivalent theory could be developed in connection with the contingent equations theory in Banach spaces presented by Shui-nee Chow and J.D. Shuur [9]. In this paper, however, we introduce some dissipativetype assumptions rather than Cesari's semicontinuity condition as in [9].

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Authors and Affiliations

  1. Institute for Information and Automatics, University of Mining and Metallurgy, Kraków, Poland

    S. Raczyński

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  1. S. Raczyński
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K. Iracki K. Malanowski S. Walukiewicz

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© 1980 Springer-Verlag

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Raczyński, S. (1980). On optimal control and reachable sets in a Banach space. In: Iracki, K., Malanowski, K., Walukiewicz, S. (eds) Optimization Techniques. Lecture Notes in Control and Information Sciences, vol 22. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036423

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  • DOI: https://doi.org/10.1007/BFb0036423

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10080-5

  • Online ISBN: 978-3-540-38248-5

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