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Abstract

We consider special boundary control systems for parabolic differential equations where the target set is described by a convex body of continuous functions. In this paper we are mainly interested in time-optimal control problems.

Keywords

Convex Body Parabolic Differential Equation Minimum Norm Problem Dann Gilt Infinite Dimensional Control 
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Literatur

  1. [1]
    BUTKOVSKIY, A.G.: Distributed control systems. New York, American Elsevier Publ.Comp. 1969.zbMATHGoogle Scholar
  2. [2]
    BUTKOVSKIY, A.G., A.I. EGOROV and K.A. LURIE: Optimal control of distributed systems (A survey of Soviet publications).SIAM J. Control 6 (1968) 437–476.Google Scholar
  3. [3]
    FALB, P.L.: Infinite dimensional control problems I: On the closure of the set of attainable states for linear systems. J. Math. Anal.Appl. 9 (1964) 12–22.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    FATTORINI, H.O.: Time-optimal control of solutions of operational differential equations.SIAM J. Control 2 (1964), 54–59.MathSciNetzbMATHGoogle Scholar
  5. [5]
    FATTORINI, H.O.: The time-optimal control problem in Banach spaces.Applied Mathematics and Optimization 1 (1974), 163–188.MathSciNetzbMATHGoogle Scholar
  6. [6]
    FRIEDMAN, A.: Optimal control for parabolic equations. J. Math. Anal.Appl. 18 (1967), 479–491.zbMATHCrossRefGoogle Scholar
  7. [7]
    FRIEDMAN, A.: Optimal control in Banach spaces. J. Math. Anal.Appl. 19 (1967), 35–55.zbMATHCrossRefGoogle Scholar
  8. [8]
    FRIEDMAN, A.: Optimal control in Banach space with fixed end-points. J. Math. Anal.Appl. 24 (1968), 161–181.MathSciNetzbMATHCrossRefGoogle Scholar
  9. [9]
    GLASHOFF, K.: Optimal control of one-dimensional linear parabolic differential equations. Erscheint in: BULIRSCH, R., W. OETTLI und J. STOER (Hrsg.): Optimierungstheorie und optimale Steuerungen, Tagungsbericht über die Oberwolfachtagung vom 18.11.-23.11.1974. Berlin-Heidelberg-New York, Springer-Verlag 19 75.Google Scholar
  10. [10]
    GLASHOFF, K.,und W. KRABS: Dualität und Bang-Bang-Prinzip bei einem parabolischen Rand-Kontrollproblem. Erscheint in: Bonner Mathematische. Schriften (1975).Google Scholar
  11. [11]
    KÖTHE, G.: Topologische lineare Räume I. 2. Aufl., Berlin-Heidelberg-New York, Springer-Verlag 1966.Google Scholar
  12. [12]
    LIONS, J.L.: Controle optimal des systemes gouvernés par des équations aux dérivées partielles.Paris, Dunod 1968.Google Scholar
  13. [13]
    LUENBERGER, D.G.: Optimization by vector space methods.New York-London-Sydney-Toronto, John Wiley and Sons 1969.Google Scholar
  14. [14]
    ROBINSON, A.C.: A survey of optimal control of distributed-parameter systems. Automatica 7 (1971), 371–388.zbMATHCrossRefGoogle Scholar
  15. [15]
    WECK, N.: Über Existenz, Eindeutigkeit und das “Bang-Bang-Prinzip” bei Kontrollproblemen aus der Wärmeleitung. Erscheint in: Bonner Mathematische Schriften (1975).zbMATHGoogle Scholar
  16. [16]
    YEGOROV, Yu.V.: Some problems in the theory of optimal control. USSR Comp.Math.Math.Phys. 3 (1963), 1209–1232.CrossRefGoogle Scholar
  17. [17]
    YOSIDA, K.: Functional analysis. 3rd ed., Berlin-Heidelberg-New York, Springer-Verlag 19 71.Google Scholar

Copyright information

© Springer Basel AG 1976

Authors and Affiliations

  • Frank Lempio
    • 1
  1. 1.Institut für Angewandte Mathematik und Statistikder Universität WürzburgD - 87 WürzburgBundesrepublik Deutschland

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