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Semi-dual approximations in optimal control

  • William W. Hager
  • George D. Ianculescu
Optimal Control: Ordinary And Delay Differential Equations
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 22)

Abstract

Tight error estimates are derived for finite element approximations to convex control problems with state and control constraints.

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References

  1. [1]
    W. E. Bosarge, Jr. and O. G. Johnson, “Error bounds of high order accuracy for the state regulator problem via piecewise polynomial approximation”, SIAM J. Control, 9 (1971), 15–28.Google Scholar
  2. [2]
    P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978.Google Scholar
  3. [3]
    W. W. Hager and S. K. Mitter, “Lagrange duality theory for convex control problems”, SIAM J. Control and Optimization, 14 (1976), 843–856.Google Scholar
  4. [4]
    W. W. Hager, “Lipschitz continuity for constrained processes”, SIAM J. Control and Optimization, 17 (1979), 321–338.Google Scholar
  5. [5]
    W. W. Hager, “The Ritz-Trefftz method for state and control constrained optimal control problems”, SIAM J. Numer. Anal., 12 (1975), 854–867.Google Scholar
  6. [6]
    W. W. Hager, “Convex control and dual approximations, part I”, Control and Cybernetics, 8 (1979), 6–22.Google Scholar
  7. [7]
    W. W. Hager, “Convex control and dual approximations, part II”, Control and Cybernetics, 8 (1979), 73–86.Google Scholar
  8. [8]
    W. W. Hager and G. Strang, “Free boundaries and finite elements in one dimension”, Math. Comp., 29 (1975), 1020–1031.Google Scholar
  9. [9]
    W. W. Hager and G. D. Ianculescu, “Semi-dual approximations in optimal control”, submitted for possible publication.Google Scholar
  10. [10]
    F. H. Mathis and G. W. Reddien, “Ritz-Trefftz approximations in optimal control”, SIAM J. Control and Optimization, 17 (1979), 307–310.Google Scholar
  11. [11]
    R. T. Rockafellar, “State constraints in convex control problems of Bolza”, SIAM J. Control, 10 (1972), 691–715.Google Scholar
  12. [12]
    G. Strang and G. Fix, An Analysis of the Finite Element Method, Prentice Hall, New York, 1973.Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • William W. Hager
    • 1
  • George D. Ianculescu
    • 2
  1. 1.Department of MathematicsCarnegie-Mellon UniversityPittsburgh
  2. 2.E. I. Du Pont de Nemours Experimental Station, E 357Wilmington

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