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 Tr. Mat. Inst. Steklova, 2001, Volume 233, Pages 5–70 (Mi tm224)

Extremal Problems for Differential Inclusions with State Constraints

S. M. Aseevab

a Steklov Mathematical Institute, Russian Academy of Sciences
b International Institute for Applied Systems Analysis

Abstract: This paper is devoted to the study of optimal control problems for differential inclusions with state constraints. The main focus is placed on the derivation of the most complete first-order necessary optimality conditions that employ the specific features of both a differential constraint given by a differential inclusion and state constraints. For the problem considered, a generalization of the Pontryagin maximum principle is obtained that strengthens many known results in this field and contains an additional condition that the Hamiltonian (the maximum function) of the problem should be stationary. For the Lagrange multipliers entering the relations of the maximum principle, the properties primarily attributed to the state constraints are studied. In particular, the degeneracy of the necessary optimality conditions is analyzed and sufficient conditions are obtained for the regularity of the Lagrange multipliers.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2001, 233, 1–63

Bibliographic databases:
UDC: 517.977

Citation: S. M. Aseev, “Extremal Problems for Differential Inclusions with State Constraints”, Differential equations. Certain mathematical problems of optimal control, Collected papers, Tr. Mat. Inst. Steklova, 233, Nauka, MAIK «Nauka/Inteperiodika», M., 2001, 5–70; Proc. Steklov Inst. Math., 233 (2001), 1–63

Citation in format AMSBIB
\Bibitem{Ase01} \by S.~M.~Aseev \paper Extremal Problems for Differential Inclusions with State Constraints \inbook Differential equations. Certain mathematical problems of optimal control \bookinfo Collected papers \serial Tr. Mat. Inst. Steklova \yr 2001 \vol 233 \pages 5--70 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm224} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1866977} \zmath{https://zbmath.org/?q=an:1013.49020} \transl \jour Proc. Steklov Inst. Math. \yr 2001 \vol 233 \pages 1--63 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Aseev S.M., Smirnov A.I., “The pontryagin maximum principle for the problem of optimally crossing a given domain”, Doklady Mathematics, 69:2 (2004), 243–245
2. Prostyakov P.V., “Construction of the reachability set of the Lotka–Volterra system”, Differential Equations, 42:3 (2006), 391–399
3. S. M. Aseev, A. V. Kryazhimskii, “The Pontryagin Maximum Principle and Optimal Economic Growth Problems”, Proc. Steklov Inst. Math., 257 (2007), 1–255
4. A. I. Smirnov, “Necessary Optimality Conditions for a Class of Optimal Control Problems with Discontinuous Integrand”, Proc. Steklov Inst. Math., 262 (2008), 213–230
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