Viability theory
Nonsmooth analysis and control theory
Nonsmooth analysis and control theory
Differential Inclusions: Set-Valued Maps and Viability Theory
Differential Inclusions: Set-Valued Maps and Viability Theory
Weak Tangency, Weak Invariance, and Carathéodory Mappings
Journal of Dynamical and Control Systems
The Construction of Differential Inclusions with Prescribed Attainable Sets
Journal of Dynamical and Control Systems
The Construction of Differential Inclusions with Prescribed Attainable Sets
Journal of Dynamical and Control Systems
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For given 驴驴驴0 and a given continuous set-valued mapping t 驴 Z(t), t 驴 [t 0, 驴], where Z(t) 驴 驴 n is a compact and convex set for every t 驴 [t 0, 驴], a differential inclusion is constructed such that the Hausdorff distance between the attainable set of the constructed differential inclusion at the instant of time t and Z(t) is less than 驴 for every t 驴 [t 0, 驴]. The right-hand side of the defined differential inclusion is affine with respect to the phase state vector and satisfies certain conditions which guarantee the existence and extendability of solutions. The solution of the problem is based on the existence of convex extensions of the affine-type convex compact set-valued mappings.