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1

Method of averaging for the system of functional-differential inclusions

100%
Janiak T., Łuczak-Kumorek E.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1996
|
tom 16
|
nr 2
137-151
EN
The basic idea of this paper is to give the existence theorem and the method of averaging for the system of functional-differential inclusions of the form ⎧$ẋ(t) ∈ F(t,x_t,y_t)$ (0) ⎨ ⎩$ẋ(t) ∈ G(t,x_t,y_t)$ (1)
2

Lower semicontinuous differential inclusions

100%
Donchev T.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1998
|
tom 18
|
nr 1-2
19-25
EN
In the paper we consider lower semicontinuous differential inclusions with one sided Lipschitz and compact valued right hand side in a Banach space with uniformly convex dual. We examine the nonemptiness and some qualitative properties of the solution set.
3
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Forward invariant sets, homogeneity and small-time local controllability

80%
Krastanov M.
Banach Center Publications
|
1995
|
tom 32
|
nr 1
287-300
EN
The property of forward invariance of a subset of $R^n$ with respect to a differential inclusion is characterized by using the notion of a perpendicular to a set. The obtained results are applied for investigating the dependence of the small-time local controllability of a homogeneous control system on parameters.
4
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On the existence of viable solutions for a class of second order differential inclusions

80%
Cernea A.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2002
|
tom 22
|
nr 1
67-78
EN
We prove the existence of viable solutions to the Cauchy problem x'' ∈ F(x,x'), x(0) = x₀, x'(0) = y₀, where F is a set-valued map defined on a locally compact set $M ⊂ R^{2n}$, contained in the Fréchet subdifferential of a ϕ-convex function of order two.
5
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A constructive method for solving stabilization problems

80%
Azhmyakov V.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2000
|
tom 20
|
nr 1
51-62
EN
The problem of asymptotic stabilization for a class of differential inclusions is considered. The problem of choosing the Lyapunov functions from the parametric class of polynomials for differential inclusions is reduced to that of searching saddle points of a suitable function. A numerical algorithm is used for this purpose. All the results thus obtained can be extended to cover the discrete systems described by difference inclusions.
6
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On differential equations and inclusions with mean derivatives on a compact manifold

80%
Azarina S., Gliklikh Y.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2007
|
tom 27
|
nr 2
385-397
EN
We introduce and investigate a new sort of stochastic differential inclusions on manifolds, given in terms of mean derivatives of a stochastic process, introduced by Nelson for the needs of the so called stochastic mechanics. This class of stochastic inclusions is ideologically the closest one to ordinary differential inclusions. For inclusions with forward mean derivatives on manifolds we prove some results on the existence of solutions.
7
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Controllability theorem for nonlinear dynamical systems

80%
Kisielewicz M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2002
|
tom 22
|
nr 2
225-232
EN
Some sufficient conditions for controllability of nonlinear systems described by differential equation ẋ = f(t,x(t),u(t)) are given.
8
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Local analysis of hybrid systems on polyhedral sets with state-dependent switching

80%
Leth J., Wisniewski R.
International Journal of Applied Mathematics and Computer Science
|
2014
|
tom 24
|
nr 2
341-355
EN
This paper deals with stability analysis of hybrid systems. Various stability concepts related to hybrid systems are introduced. The paper advocates a local analysis. It involves the equivalence relation generated by reset maps of a hybrid system. To establish a tangible method for stability analysis, we introduce the notion of a chart, which locally reduces the complexity of the hybrid system. In a chart, a hybrid system is particularly simple and can be analyzed with the use of methods borrowed from the theory of differential inclusions. Thus, the main contribution of this paper is to show how stability of a hybrid system can be reduced to a specialization of the well established stability theory of differential inclusions. A number of examples illustrate the concepts introduced in the paper.
9

Co-density and other properties of the solution set of differential inclusions with noncompact right-hand side

80%
Goncharov V.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1996
|
tom 16
|
nr 2
103-120
EN
There are studied two classes of differential inclusions with right-hand side admitting noncompact values in a Banach space. Co-density, lower semicontinuity in initial point and relaxation property of the solution set have been obtained.
10

Some remarks on boundary value problem for differential inclusions

80%
Kisielewicz M.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1997
|
tom 17
|
nr 1-2
43-49
EN
Some sufficient conditions for the existence of solutions to boundary value problem for differential inclusions are given.
11
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A study of second order differential inclusions with four-point integral boundary conditions

71%
Ahmad B., Ntouyas S.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2011
|
tom 31
|
nr 2
137-156
EN
In this paper, we discuss the existence of solutions for a four-point integral boundary value problem of second order differential inclusions involving convex and non-convex multivalued maps. The existence results are obtained by applying the nonlinear alternative of Leray Schauder type and some suitable theorems of fixed point theory.
12
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On differential inclusions of velocity hodograph type with Carathéodory conditions on Riemannian manifolds

71%
Gliklikh Y., Obukhovski A.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2004
|
tom 24
|
nr 1
41-48
EN
We investigate velocity hodograph inclusions for the case of right-hand sides satisfying upper Carathéodory conditions. As an application we obtain an existence theorem for a boundary value problem for second-order differential inclusions on complete Riemannian manifolds with Carathéodory right-hand sides.
13
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A Tikhonov-type theorem for abstract parabolic differential inclusions in Banach spaces

71%
Gudovich A., Kamenski M., Nistri P.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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2001
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tom 21
|
nr 2
207-234
EN
We consider a class of singularly perturbed systems of semilinear parabolic differential inclusions in infinite dimensional spaces. For such a class we prove a Tikhonov-type theorem for a suitably defined subset of the set of all solutions for ε ≥ 0, where ε is the perturbation parameter. Specifically, assuming the existence of a Lipschitz selector of the involved multivalued maps we can define a nonempty subset $Z_L(ε)$ of the solution set of the singularly perturbed system. This subset is the set of the Hölder continuous solutions defined in [0,d], d > 0 with prescribed exponent and constant L. We show that $Z_L(ε)$ is uppersemicontinuous at ε = 0 in the C[0,d]×C[δ,d] topology for any δ ∈ (0,d].
14

Compactness in certain abstract function spaces with application to differential inclusions

61%
Ahmed N.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1995
|
tom 15
|
nr 1
75-94
EN
In this note we present a result on compactness in certain Banach spaces of vector valued functions. We demonstrate an application of this result to the questions of existence of solutions of nonlinear differential inclusions on a Banach space.
15
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Partially dissipative periodic processes

61%
Andres J., Górniewicz L., Lewicka M.
Banach Center Publications
|
1996
|
tom 35
|
nr 1
109-118
EN
Further extension of the Levinson transformation theory is performed for partially dissipative periodic processes via the fixed point index. Thus, for example, the periodic problem for differential inclusions can be treated by means of the multivalued Poincaré translation operator. In a certain case, the well-known Ważewski principle can also be generalized in this way, because no transversality is required on the boundary.
16
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Controllability of evolution equations and inclusions driven by vector measures

61%
Ahmed N. U.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2004
|
tom 24
|
nr 1
49-72
EN
In this paper, we consider the question of controllability of a class of linear and semilinear evolution equations on Hilbert space with measures as controls. We present necessary and sufficient conditions for weak and exact (strong) controllability of a linear system. Using this result we prove that exact controllability of the linear system implies exact controllability of a perturbed semilinear system. Controllability problem for the semilinear system is formulated as a fixed point problem on the space of vector measures and is concluded controllability from the existence of a fixed point. Our results cover impulsive controls as well as regular controls.
17

Compactness in certain abstract function spaces with application to differential inclusions

61%
Ahmed N.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
1995
|
tom 15
|
nr 1
21-28
EN
In this note we present a result on compactness in certain Banach spaces of vector valued functions. We demonstrate an application of this result to the questions of existence of solutions of nonlinear differential inclusions on a Banach space.
18
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Impulsive perturbation of C₀-semigroups and stochastic evolution inclusions

61%
Ahmed N.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2002
|
tom 22
|
nr 1
125-149
EN
In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions. We prove existence of solutions and study properties of the solution set. It is also indicated how these results can be used in the study of control systems driven by vector measures.
19
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Existence results for impulsive semilinear fractional differential inclusions with delay in Banach spaces

61%
Hammouche H., Guerbati K., Benchohra M., Abada N.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2013
|
tom 33
|
nr 2
149-170
EN
In this paper, we introduce a new concept of mild solution of some class of semilinear fractional differential inclusions of order 0 < α < 1. Also we establish an existence result when the multivalued function has convex values. The result is obtained upon the nonlinear alternative of Leray-Schauder type.
20
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Optimal control of impulsive stochastic evolution inclusions

61%
Ahmed N.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2002
|
tom 22
|
nr 2
155-184
EN
In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions driven by vector measures. We use stochastic vector measures as controls adapted to an increasing family of complete sigma algebras and prove the existence of optimal controls.
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