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Pontryagin’s maximum principle for multiple integrals

  • Rolf Klötzler
III Optimal Control III.1 Control Problems
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 180)

Keywords

Multiple Integral Distributional Sense Pontryagin Maximum Principle Sufficient Optimality Condition Multiplier Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Cesari, L.: Optimization with partial differential equations in Dieudonné-Rashevsky form and conjugate problems, Arch.Rat.Mech.Anal. 33 (1969), 339–357.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Ekeland, I., Temam, R.: Analyse convexe et problèmes variationnels, Dunod et Gauthier-Villars,Paris 1974.zbMATHGoogle Scholar
  3. [3]
    Hestenes, M.R.: Calculus of Variations and Optimal Control, John Wiley & Sons, INC, New York,London, Sidney 1966.zbMATHGoogle Scholar
  4. [4]
    Ioffe, A.D., Tichomirov, W.M.: Theory of Extremal Problems [Russ.], Nauka,Moscow 1974.Google Scholar
  5. [5]
    Ioffe, A.D., Tichomirov, W.M.: Extensions of Variational Problems [Russ.], Trudy Mosc.Mat.Obscht. 18 (1968), 187–246.zbMATHGoogle Scholar
  6. [6]
    Kantorowitsch, L.W., Akilow, G.P.: Funktionalanalysis in normierten Räumen, Akademie-Verlag Berlin 1964.zbMATHGoogle Scholar
  7. [7]
    Klötzler, R.: On Pontryagin’s maximum principle for multiple integrals, Beiträge zur Analysis 8 (1976), 67–75.Google Scholar
  8. [8]
    Klötzler, R.: On a general conception of duality in optimal control, Lecture Notes in Math. 703 (1979), 189–196.CrossRefGoogle Scholar
  9. [9]
    Krotov, W.F., Gurman, W.I.: Methods and Problems of the Optimal Control [Russ.], Nauka,Moscow 1973.Google Scholar
  10. [10]
    Pontryagin, L.S., Boltjanskij, W.G., Gamkrelidze, R.W., Miscenko, E.F.: Mathematical Theory of Optimal Processes [Russ.], Gos.Izd.,Moscow 1961.Google Scholar
  11. [11]
    Rockafellar, R.T.: Existence and duality theorems for convex problems of Bolza, Trans.Amer.Math.Soc. 159 (1971), 1–40.zbMATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    Rolewicz, S.: Functional Analysis and Control Theory, D. Reidel Publishing Comp./ PWN-Polish Scientific Publishers, Dordrecht,Boston,Lancaster,Tokyo,Warsaw 1987zbMATHGoogle Scholar
  13. [13]
    Rund, H.: Pontryagin functions for multiple integral control problems, J.Optim.Theory Appl. 18 (1976), 511–520.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© International Federation for Information Processing 1992

Authors and Affiliations

  • Rolf Klötzler
    • 1
  1. 1.Sektion MathematikUniversität LeipzigLeipzig

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