Kh.G. Guseinov

On differential inclusions with prescribed attainable sets

Abstract In this article, the inverse problem of the differential inclusion theory is studied. For a given e >0 and a continuous set valued map t → W ( t ), t ∈[ t 0 , θ ], where W ( t )⊂ R n is compact and convex for every t ∈[ t 0 , θ ], it is required to define differential inclusion so that the Hausdorff distance between the attainable set of the differential inclusion at the time moment t with initial set ( t 0 , W ( t 0 )) and W ( t ) would be less than e for every t ∈[ t 0 , θ ].

On the coincidence of maximal stable bridges in two approach game problems for stationary control systems

Two approach game problems with a compact target set on a finite time interval are studied. The coincidence of their solutions is investigated.

On the coincidence of maximal stable bridges in two game problems

We consider a conflict control system on a finite time interval governed by an ordinary differential equation. More specifically, we study and compare two game problems describing the system approaching a terminal set M in the state space of the system [1]. In one of these problems, the first player uses a feedback control to ensure that the state vector of the system reaches M at the terminal time. In the other problem, a feedback control is used to ensure that the state vec� tor of the system reaches M no later than at the termi� nal time. In the approach proposed in [1], the central elements of the solving construction in both problems

On the Directional Differentiability Properties of the Marginal Function 1

Abstract In this paper, by using the directional lower and upper derivative of a set-valued map, the directional lower and upper derivatives of marginal function are investigated. Sufficient condition, ensuring the existence of the directionalderivative of the marginal function is obtained.

On Solution of Boundary Value Problem for Differential Inclusion1

Abstract In the article an inverse problem for differential inclusion is considered. For a given compact set M*⊂ Rn it is required to define the maximal set M0⊂ Rn so that the reachable set of differential inclusion with initial set (t0, M0) would be contained in the given set M* at the time moment θ. The approximation method for construction of the set M0 is proposed which is step by step backward procedure.