On optimal control and reachable sets in a Banach space

  • S. Raczyński
Optimal Control: Partial Differential Equations
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 22)


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].


Banach Space Optimal Control Problem Optimal Trajectory Trol System Measurable Selector 
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Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • S. Raczyński
    • 1
  1. 1.Institute for Information and AutomaticsUniversity of Mining and MetallurgyKrakówPoland

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