On differential inclusions with prescribed attainable sets

In this article the existence of the convex extension of convex set valued map is considered. Conditions are obtained, based on the notion of the derivative of set valued maps, which guarantee the existence of convex extension. The conditions are given, when the convex set valued map has no convex extension. The convex set valued map is specified, which is the maximal convex extension of the given convex set valued map and includes all other convex extensions. The connection between Lipschitz continuity and existence of convex extension of the given convex set valued map is studied.

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On the continuity property of Lp balls and an application

Guseinov

Nazlipinar

2007

Journal of Mathematical Analysis and Applications

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In this paper continuity properties of the set-valued map p → B p (μ 0 ), p ∈ (1, +∞), are considered where B p (μ 0 ) is the closed ball of the space L p ([t 0 , θ]; R m ) centered at the origin with radius μ 0 . It is proved that the set-valued map p → B p (μ 0 ), p ∈ (1, +∞), is continuous. Applying obtained results, the attainable set of the nonlinear control system with integral constraint on the control is studied. The admissible control functions are chosen from B p (μ 0 ). It is shown that the attainable set of the system is continuous with respect to p.

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On differential inclusions with prescribed attainable sets

Cited by 4 publications

References 8 publications

The Construction of Differential Inclusions with Prescribed Attainable Sets

The Construction of Differential Inclusions with Prescribed Attainable Sets

Convex extensions of the convex set valued maps

On the continuity property of Lp balls and an application

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