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This article is cited in 4 scientific papers (total in 4 papers)
Hessian of the solution of the Hamilton–Jacobi equation in the theory of extremal problems
M. I. Zelikin M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
An optimal control problem with separated conditions at the end-points
is studied. It is assumed that
there exists on the manifold of left end-points
(as well as on the manifold of right end-points) a field of extremals
containing the fixed extremal.
A criterion describing necessary and sufficient
conditions of optimality in terms of these two fields is proved.
The sufficient condition is the positive-definiteness of the difference of the solutions of the
corresponding matrix Riccati's equations and the necessary one is its non-negativity.
The key part in the proof of the criterion is played by a formula relating
the solution of Riccati's equation and the Hessian of the Bellman function.
Received: 24.12.2003
Citation:
M. I. Zelikin, “Hessian of the solution of the Hamilton–Jacobi equation in the theory of extremal problems”, Mat. Sb., 195:6 (2004), 57–70; Sb. Math., 195:6 (2004), 819–831
Linking options:
https://www.mathnet.ru/eng/sm826https://doi.org/10.1070/SM2004v195n06ABEH000826 https://www.mathnet.ru/eng/sm/v195/i6/p57
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Abstract page: | 597 | Russian version PDF: | 256 | English version PDF: | 17 | References: | 44 | First page: | 3 |
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