Journal of Mathematical Sciences

, Volume 135, Issue 4, pp 3125–3144 | Cite as

Lagrangian submanifold landscapes of necessary conditions for maxima in optimal control: Global parameterizations and generalized solutions

  • B. Piernicola
  • C. Franco
Article

Abstract

We construct global generating functions of the initial and of the evolution Lagrangian submanifolds related to a Hamiltonian flow. These global parameterizations are realized by means of Amann—Conley—Zehnder reduction. In some cases, we have to to face generating functions that are weakly quadratic at infinity; more precisely, degeneracy points can occurs. Therefore, we develop a theory which allows us to treat possibly degenerate cases in order to define a Chaperon—Sikorav—Viterbo weak solution of a time-dependent Hamilton-Jacobi equation with a Cauchy condition given at time t = T (T > 0). The starting motivation is to study some aspects of Mayer problems in optimal control theory.

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • B. Piernicola
    • 1
  • C. Franco
    • 2
  1. 1.SISSA/ISASTriesteItaly
  2. 2.Dipartimento di Matematica Pura ed ApplicataUniversitá degli Studi di PadovaPadovaItaly

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