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Wyświetlanie 1-15 z 46
Tytuł:
Weak solutions of stochastic differential inclusions and their compactness
Autorzy:
Michta, Mariusz
Powiązania:
https://bibliotekanauki.pl/articles/729384.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
semimartingale
stochastic differential inclusions
weak solutions
martingale problem
weak convergence of probability measures
Opis:
In this paper, we consider weak solutions to stochastic inclusions driven by a semimartingale and a martingale problem formulated for such inclusions. Using this we analyze compactness of the set of solutions. The paper extends some earlier results known for stochastic differential inclusions driven by a diffusion process.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2009, 29, 1; 91-106
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Viability theory: an applied mathematics tool for achieving dynamic systems sustainability
Autorzy:
Krawczyk, Jacek B.
Pharo, Alastair S.
Powiązania:
https://bibliotekanauki.pl/articles/748128.pdf
Data publikacji:
2013
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
viability theory, differential inclusions, sustainability
Opis:
 Sustainability is considered an issue of paramount importance; yet scientists andpoliticians still seek to understand what it means, practically and conceptually, tobe sustainable. This paper's aim is to introduce viability theory, a relativelyyoung branch of continuous mathematics which provides a conceptual frameworkthat is very well suited to sustainability problems.  In particular, viability theory can be used toanswer important questions about the sustainability of systems, including thosestudied in macroeconomics, and can be used to determine sustainable policies fortheir management.  The principal analytical tool of viability theory is theviability kernel which is the set of all state-space points such that it is possible for evolutions starting from each of those points to remain within the system's predetermined constraints indefinitely. Although, in some circumstances,  kernel determinationcan be performed analytically,  most practical results in viability theory rely on graphical approximations of viability kernels,which for nonlinear and high-dimensional problems can only be approached numerically.This paper provides an outline of the coreconcepts of viability theory and an overview of the numerical approachesavailable for computing approximate viability kernels.  \vikaasa{}, aspecialised software application developed by the authors and designed tocompute such approximate viability kernels is presented along-side examples ofviability theory in action in the spheres of bio-economics and macroeconomics.
Źródło:
Mathematica Applicanda; 2013, 41, 1
1730-2668
2299-4009
Pojawia się w:
Mathematica Applicanda
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Systems of differential inclusions in the absence of maximum principles and growth conditions
Autorzy:
Tisdell, Christopher
Powiązania:
https://bibliotekanauki.pl/articles/729443.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
boundary value problem
systems of differential inclusions
existence of solutions
a priori bounds
two-point boundary conditions
three-point boundary conditions
Opis:
This article investigates the existence of solutions to second-order boundary value problems (BVPs) for systems of ordinary differential inclusions. The boundary conditions may involve two or more points. Some new inequalities are presented that guarantee a priori bounds on solutions to the differential inclusion under consideration. These a priori bound results are then applied, in conjunction with appropriate topological methods, to prove some new existence theorems for solutions to systems of BVPs for differential inclusions. The new conditions allow the treatment of systems of BVPs in the absence of maximum principles and growth conditions. The results are also new for differential equations involving Carathéodory or even continuous right-hand sides.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2006, 26, 1; 129-141
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stochastic differential inclusions of Langevin type on Riemannian manifolds
Autorzy:
Gliklikh, Yuri
Obukhovskiĭ, Andrei
Powiązania:
https://bibliotekanauki.pl/articles/729326.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
stochastic differential inclusions
Langevin equation
Riemannian manifolds
Opis:
We introduce and investigate a set-valued analogue of classical Langevin equation on a Riemannian manifold that may arise as a description of some physical processes (e.g., the motion of the physical Brownian particle) on non-linear configuration space under discontinuous forces or forces with control. Several existence theorems are proved.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2001, 21, 2; 173-190
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some optimal control problems for partial differential inclusions
Autorzy:
Kisielewicz, M.
Powiązania:
https://bibliotekanauki.pl/articles/255397.pdf
Data publikacji:
2008
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
partial differential inclusions
diffusion processes
existence theorems
Opis:
Partial differential inclusions are considered. In particular, basing on diffusions properties of weak solutions to stochastic differential inclusions, some existence theorems and some properties of solutions to partial differential inclusions are given.
Źródło:
Opuscula Mathematica; 2008, 28, 4; 507-516
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some averaging results for ordinary differential inclusions
Autorzy:
Bourada, Amel
Guen, Rahma
Lakrib, Mustapha
Yadi, Karim
Powiązania:
https://bibliotekanauki.pl/articles/729511.pdf
Data publikacji:
2015
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
ordinary differential inclusions
averaging method
Opis:
We consider ordinary differential inclusions and we state and discuss some averaging results for these inclusions. Our results are proved under weaker conditions than the results in the literature.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2015, 35, 1; 47-63
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Solution tubes to differential inclusions within a collection of sets
Autorzy:
Quincampoix, M.
Veliov, V.
Powiązania:
https://bibliotekanauki.pl/articles/206199.pdf
Data publikacji:
2002
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
estymacja deterministyczna
system niepewny
system sterowania
control systems
deterministic estimation
differential inclusions
reachable sets
uncertain systems
Opis:
This paper develops the theory of solution tubes to differential inclusions (uncertain systems) within a prescribed collection of sets. The notion is defined as a minimal invariant tube with values in the collection. Under certain requirements for the collection we prove existence and Lipschitz-like stability of the solution tubes. The theory is relevant to problems of systems estimation in the context of control or differential games.
Źródło:
Control and Cybernetics; 2002, 31, 3; 847-862
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Partially dissipative periodic processes
Autorzy:
Andres, Jan
Górniewicz, Lech
Lewicka, Marta
Powiązania:
https://bibliotekanauki.pl/articles/1358930.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
large-period forced oscillations
partial dissipativity
Poincaré translation operator
fixed point index
differential inclusions
Periodic processes
Opis:
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.
Źródło:
Banach Center Publications; 1996, 35, 1; 109-118
0137-6934
Pojawia się w:
Banach Center Publications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal control of impulsive stochastic evolution inclusions
Autorzy:
Ahmed, N.
Powiązania:
https://bibliotekanauki.pl/articles/729552.pdf
Data publikacji:
2002
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
impulsive perturbations
C₀-semigroups
stochastic systems
differential inclusions
vector measures
optimal controls
Opis:
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.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2002, 22, 2; 155-184
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal control of delay-differential inclusions with multivalued initial conditions in infinite dimensions
Autorzy:
Mordukhovich, B. S.
Wang, D.
Wang, L.
Powiązania:
https://bibliotekanauki.pl/articles/969562.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
discrete approximations
optimal control
variational analysis
endpoint constraints
delay-differential inclusions
multivalued initial conditions
extended Euler-Lagrange formalism
generalized differentiation
Banach and Asplund spaces
necessary optimality conditions
Opis:
This paper is devoted to the study of a general class of optimal control problems described by delay-differential inclusions with infinite-dimensional state spaces, endpoints constraints, and multivalued initial conditions. To the best of our knowledge, problems of this type have not been considered in the literature, except for some particular cases when either the state space is finite-dimensional or there is no delay in the dynamics. We develop the method of discrete approximations to derive necessary optimality conditions in the extended Euler-Lagrange form by using advanced tools of variational analysis and generalized differentiation in infinite dimensions. This method consists of the three major parts: (a) constructing a well-posed sequence of discrete-time problems that approximate in an appropriate sense the original continuous-time problem of dynamic optimization; (b) deriving necessary optimality conditions for the approximating discrete-time problems by reducing them to infinite-dimensional problems of mathematical programming and employing then generalized differential calculus; (c) passing finally to the limit in the obtained results for discrete approximations to establish necessary conditions for the given optimal solutions to the original problem. This method is fully realized in the delay-differential systems under consideration.
Źródło:
Control and Cybernetics; 2008, 37, 2; 393-428
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal control of constrained delay-differential inclusions with multivalued initial conditions
Autorzy:
Mordukhovich, B. S.
Wang, L.
Powiązania:
https://bibliotekanauki.pl/articles/970519.pdf
Data publikacji:
2003
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
aproksymacja dyskretna
warunek konieczny optymalności
analiza wariacyjna
stabilność
optymalizacja niegładka
różniczkowanie uogólnione
delay-differential inclusions
discrete approximations
necessary optimality conditions
variational analysis
stability
nonsmooth optimization
generalized differentiation
Opis:
This paper studies a general optimal control problem for nonconvex delay-differential inclusions with endpoint constraints. In contrast to previous publications on this topic, we incorporate time-dependent set constraints on the initial interval, which are specific for systems with delays and provide an additional source for optimization. Our variational analysis is based on well-posed discrete approximations of constrained delay-differential inclusions by a family of time-delayed systems with discrete dynamics and perturbed constraints. Using convergence results for discrete approximations and advanced tools of nonsmooth variational analysis, we derive necessary optimality conditions for constrained delay-differential inclusions in both Euler-Lagrange and Hamiltonian forms involving nonconvex generalized differential constructions for nonsmooth functions, sets, and set-valued mappings.
Źródło:
Control and Cybernetics; 2003, 32, 3; 585-609
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the theorem of Filippov-Pliś and some applications
Autorzy:
Donchev, T.
Farkhi, E.
Powiązania:
https://bibliotekanauki.pl/articles/970906.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
differential inclusions
one-sided
Lipschitz
Filippov
Plis
Opis:
In the paper some known and new extensions of the famous theorem of Filippov (1967) and a theorem of Plis (1965) for differential inclusions are presented. We replace the Lipschitz condition on the set-valued map in the right-hand side by a weaker onesided Lipschitz (OSL), one-sided Kamke (OSK) or a continuity-like condition (CLC). We prove new Filippov-type theorems for singularly perturbed and evolution inclusions with OSL right-hand sides. In the CLC case we obtain two extended theorems, one of which implies directly the relaxation theorem. We obtain also a theorem in Banach spaces for OSK multifunctions. Some applications to exponential formulae are surveyed.
Źródło:
Control and Cybernetics; 2009, 38, 4A; 1251-1271
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the existence of viable solutions for a class of second order differential inclusions
Autorzy:
Cernea, Aurelian
Powiązania:
https://bibliotekanauki.pl/articles/729526.pdf
Data publikacji:
2002
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
viable solutions
ϕ-monotone operators
differential inclusions
Opis:
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.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2002, 22, 1; 67-78
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On differential inclusions of velocity hodograph type with Carathéodory conditions on Riemannian manifolds
Autorzy:
Gliklikh, Yuri
Obukhovski, Andrei
Powiązania:
https://bibliotekanauki.pl/articles/729628.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
differential inclusions
Carathéodory conditions
velocity hodograph
Riemannian manifold
two-point bounadry value problem
Opis:
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.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2004, 24, 1; 41-48
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On differential equations and inclusions with mean derivatives on a compact manifold
Autorzy:
Azarina, S.
Gliklikh, Yu.
Powiązania:
https://bibliotekanauki.pl/articles/729459.pdf
Data publikacji:
2007
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
mean derivatives
differential inclusions
stochastic processes on manifolds
Opis:
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.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2007, 27, 2; 385-397
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 46

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