On a Control Problem with Incomplete Information: Quasistrategies and Control Procedures with a Model

Khlopin, D. V.; Ченцов, А. Г.

doi:10.1007/s10625-006-0009-0

Cited by 3 publications

(3 citation statements)

References 9 publications

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“…This approach is similar to the traditional one proposed in [5,7,8] and developed by N.N. Krasovskii and by his followers [9,10]. …”

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confidence: 77%

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On question about extension of maximin problem with phase constraints

Baklanov¹

2013

ams

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We study the asymptotic behavior of maximin values of a payoff function, when relaxed constraints are tightened. The payoff function depends on the trajectories of controlled systems of the first and second player. An extension in the class of the Radon measures is used. The asymptotic equivalence between two types of the constraints relaxations is shown. Mathematics Subject Classification: 46N10, 49J35, 49J45, 49N99Keywords: Radon measures, extension, relaxation of constraints, maximin, asymptotic equivalenceWe study the asymptotic behavior of maximin values of a payoff function, when relaxed constraints are tightened. The payoff function depends on the trajectories of controlled systems of the first and second player. These systems can be non-linear; this is the important distinction from earlier papers [1,2], where various asymptotic effects for linear systems with impulse constraints were considered and an extension in the class of finitely additive measures was used (see also [3,4]). In the present paper a different approach is used (see [6]). We implement an extension in the class of the Radon measures. This approach is similar to the traditional one proposed in [5,7,8] and developed by N.N. Krasovskii and by his followers [9,10].

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“…This approach is similar to the traditional one proposed in [5,7,8] and developed by N.N. Krasovskii and by his followers [9,10]. …”

mentioning

confidence: 77%

“…To prove this, we used continuity of (7) and (8)- (10). Theorem 1 shows the presentations of attraction sets in spaces of trajectories of (1) and (2).…”

Section: Theorem 1 the Following Equations Holdmentioning

confidence: 99%

On question about extension of maximin problem with phase constraints

Baklanov¹

2013

ams

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“…Obviously, game problems require extensions [4]. These problems can be divided into two types: those for which it is possible to well define an extension only on the product of ordinary controls sets of players [4][5][6], and those for which it is sufficient to construct an extension of an ordinary controls set for each player separately [7][8][9][10]. If we deals with a maximin problem of the second type, then we can use the following representation of the maximin value V ext after an extension:…”

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confidence: 99%

Purely finitely additive measures as generalized elements in a maximin problem

Baklanov¹

2013

ams

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We study the asymptotic behavior of maximin values of a payoff function, when admissible controls tend to infinity. The payoff function is superposition of a continuos function and a function that is uniform limit of step functions. An extension in the class of finitely additive measures is used. Mathematics Subject Classification: 46N10, 49J35, 49J45, 49N99Keywords: purely finitely additive measures, extension, maximin.It is natural in control problems to use extensions constructions due to the non-existence of optimal solutions [1]. Moreover, extensions are needed for a 'regularization' of practically interesting problems that are associated with asymptotic relaxations of constraints (see [2,3]). Obviously, game problems require extensions [4]. These problems can be divided into two types: those for which it is possible to well define an extension only on the product of ordinary controls sets of players [4][5][6], and those for which it is sufficient to construct an extension of an ordinary controls set for each player separately [7][8][9][10]. If we deals with a maximin problem of the second type, then we can use the following representation of the maximin value V ext after an extension:

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The Method of Comparison with a Model Equation in the Study of Inclusions in Vector Metric Spaces

Zhukovskiy,

Panasenko

2024

Proc. Steklov Inst. Math.

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On a Control Problem with Incomplete Information: Quasistrategies and Control Procedures with a Model

Cited by 3 publications

References 9 publications

On question about extension of maximin problem with phase constraints

On question about extension of maximin problem with phase constraints

Purely finitely additive measures as generalized elements in a maximin problem

The Method of Comparison with a Model Equation in the Study of Inclusions in Vector Metric Spaces

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