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Invariance of the Hamiltonian in Control Problems for Semilinear Parabolic Distributed Parameter Systems

  • H. O. Fattorini
Conference paper
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 118)

Abstract

We consider a general optimal control problem for a distributed parameter described by a semilinear parabolic equation. We show that the Hamiltonian is invariant over optimally controlled trajectories, and that it vanishes when the terminal time is free. The method is that of approximation of the original control system by a sequence of “smoothed” control systems

1991 Mathematics Subject Classification

93E20 93E25 

Key words and phrases

Lagrange multiplier rule Kuhn-Tucker conditions maximum principle optimal control 

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Copyright information

© Springer Basel AG 1994

Authors and Affiliations

  • H. O. Fattorini
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaLos AngelesUSA

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