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Izv. RAN. Ser. Mat., 1998, Volume 62, Issue 5, Pages 79–102 (Mi izv211)  

This article is cited in 2 scientific papers (total in 2 papers)

Non-traditional conditions for the existence of an optimal control for the Goursat–Darboux equations

O. A. Danilova, A. S. Matveev


Abstract: We consider the optimal control problem for the non-linear Goursat–Darboux equations in the case when the quality functional depends only on the phase variable. We show that a natural analogue of the “traditional” criterion for the existence of an optimal control for this problem is not valid. Under certain assumptions on the equations we obtain necessary and sufficient conditions under which any functional of the type mentioned above attains a minimum. The traditional condition (the convexity of the set of contingencies) is supplemented here by the following essential condition: the right-hand side of the differential equation is affine with respect to each of the two lowest derivatives of the phase variable.

DOI: https://doi.org/10.4213/im211

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English version:
Izvestiya: Mathematics, 1998, 62:5, 929–951

Bibliographic databases:

MSC: 49J99, 49J45
Received: 27.05.1996

Citation: O. A. Danilova, A. S. Matveev, “Non-traditional conditions for the existence of an optimal control for the Goursat–Darboux equations”, Izv. RAN. Ser. Mat., 62:5 (1998), 79–102; Izv. Math., 62:5 (1998), 929–951

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. S. Gavrilov, M. I. Sumin, “Parametric optimization of nonlinear Goursat–Darboux systems with phase constraints”, Comput. Math. Math. Phys., 44:6 (2004), 949–968  mathnet  mathscinet  zmath
    2. V. S. Gavrilov, M. I. Sumin, “A parametric problem of the suboptimal control of the Goursat–Darboux system with a pointwise phase constraint”, Russian Math. (Iz. VUZ), 49:6 (2005), 37–48  mathnet  mathscinet  zmath  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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