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Wyświetlanie 1-15 z 21
Tytuł:
Electrical impedance tomography: from topology to shape
Autorzy:
Hintermuller, M.
Laurain, A.
Powiązania:
https://bibliotekanauki.pl/articles/970303.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
electrical impedance tomography
inverse problem
shape derivative
topological derivative
level set method
Opis:
A level set based shape and topology optimization approach to electrical impedance tomography (EIT) problems with piecewise constant conductivities is introduced. The proposed solution algorithm is initialized by using topological sensitivity analysis. Then it relies on the notion of shape derivatives to update the shape of the domains where conductivity takes different values.
Źródło:
Control and Cybernetics; 2008, 37, 4; 913-933
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Topological derivative for optimal control problems
Autorzy:
Sokołowski, J.
Żochowski, A.
Powiązania:
https://bibliotekanauki.pl/articles/206790.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowanie optymalne
asymptotic expansion
control problems
shape derivative
shape optimization
topological derivative
Opis:
The topological derivative is introduced for the extremal values of cost functionals for control problems. The optimal control problem considered in the paper is defined for the elliptic equation which models the deflection of an elastic membrane. The derivative measures the sensitivity of the optimal value of the cost with respect to changes in topology. A change in topology means removing a small ball from the interior of the domain of integration. The topological derivative can be used for obtaining the numerical solutions of the shape optimization problems.
Źródło:
Control and Cybernetics; 1999, 28, 3; 611-625
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On shape sensitivity analysis of the cost functional without shape sensitivity of the state variable
Autorzy:
Kasumba, H.
Kunisch, K.
Powiązania:
https://bibliotekanauki.pl/articles/206115.pdf
Data publikacji:
2011
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
shape derivative
Navier-Stokes equations
cost functional
Opis:
A general framework for calculating shape derivatives for domain optimization problems with partial differential equations as constraints is presented. The first order approximation of the cost with respect to the geometry perturbation is arranged in an efficient manner that allows the computation of the shape derivative of the cost without the necessity to involve the shape derivative of the state variable. In doing so, the state variable is only required to be Lipschitz continuous with respect to geometry perturbations. Application to shape optimization with the Navier-Stokes equations as PDE constraint is given.
Źródło:
Control and Cybernetics; 2011, 40, 4; 989-1017
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Shape derivatives for general objective functions and the incompressible Navier-Stokes equations
Autorzy:
Schmidt, S.
Schulz, V.
Powiązania:
https://bibliotekanauki.pl/articles/969869.pdf
Data publikacji:
2010
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
shape optimization
shape derivative
Navier-Stokes
adjoint calculus
Opis:
The aim of this paper is to present the shape derivative for a wide array of objective functions using the incompressible Navier-Stokes equations as a state constraint. Most real world applications of computational fluid dynamics are shape optimization problems in nature, yet special shape optimization techniques are seldom used outside the field of elliptic partial differential equations and linear elasticity. This article tries to be self contained, also presenting many useful results from the literature. We conclude with a comparison of different objective functions for the shape optimization of an obstacle in a channel, which can be done quite conveniently when one knows the general form of the shape gradient.
Źródło:
Control and Cybernetics; 2010, 39, 3; 677-713
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Shape differentiability of the Neumann problem of the Laplace equation in the half-space
Autorzy:
Amrouche, C.
Necasova, S.
Sokołowski, J.
Powiązania:
https://bibliotekanauki.pl/articles/970287.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
shape optimization
Neumann problem
unbounded domain
material derivative
Opis:
We deal with the existence of the material derivative of the Laplace equation with the Neumann boundary condition in the half space. We consider two different perturbations of domains to get the existence of weak Gateaux material derivative and the existence of Fréchet material derivatives.
Źródło:
Control and Cybernetics; 2008, 37, 4; 747-769
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
An existence theorem for set differential inclusions in a semilinear metric space
Autorzy:
De Blasi, F. S.
Lakshmikantham, V.
Bhaskar, T. G.
Powiązania:
https://bibliotekanauki.pl/articles/970280.pdf
Data publikacji:
2007
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
approximate continuous selections
Cauchy problem
set differential inclusions
Hukuhara derivative
Opis:
Using the notion of continuous approximate selections, we establish an existence theorem for set differential inclusions in a semi-linear metric space.
Źródło:
Control and Cybernetics; 2007, 36, 3; 571-582
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Generalized J-integral method for sensitivity analysis of static shape design
Autorzy:
Ohtsuka, K.
Chludnev, A.
Powiązania:
https://bibliotekanauki.pl/articles/205915.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
derivative of energy functional
domain perturbation
GJ-integral
sensitivity analysis
Opis:
The paper analyses the concept of GJ-integral. This concept is linked with the derivative of the energy functional with respect to a general perturbation of the domain and it is useful in studying many problems of sensitivity analysis. Applications of the GJ-integral method to numerous linear and nonlinear problems are indicated.
Źródło:
Control and Cybernetics; 2000, 29, 2; 513-533
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stabilization of multivariable linear time-invariant systems by proportional-plus-derivative state feedback
Autorzy:
Kiritsis, Konstadinos H.
Powiązania:
https://bibliotekanauki.pl/articles/31342764.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
stabilization
proportional-plus-derivative state feedback
linear time-invariant systems
Opis:
This paper is devoted to the study of the problem of stabilization by proportional-plus-derivative state feedback for multivariable linear time-invariant systems. In particular, explicit necessary and sufficient conditions are established for the stability of a closed-loop system obtained by proportional-plus-derivative state feedback from the given multivariable linear time-invariant system. A procedure is given for the computation of stabilizing proportional- plus-derivative state feedback. Our approach is based on properties of real and polynomial matrices.
Źródło:
Control and Cybernetics; 2023, 52, 1; 53-77
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Growth control of cracks under contact conditions based on the topological derivative of the Rice’s integral
Autorzy:
da Silva Xavier, Marcel Duarte
Novotny, Antonio André
Sokołowski, Jan
Powiązania:
https://bibliotekanauki.pl/articles/1839141.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
Rice’s integral
Griffith’s criterion
Eshelby’s tensor
topological derivative
Opis:
In the present paper we propose a simple method for dealing with growth control of cracks under contact type boundary conditions on their lips. The aim is to find a mechanism for decreasing the energy release rate of cracked components, which means increasing their fracture toughness. The method consists in minimizing a shape functional defined in terms of the Rice’s integral, with respect to the nucleation of hard and/or soft inclusions, according to the information provided by the associated topological derivative. Based on Griffith’s energy criterion, this simple strategy allows for an increase in fracture toughness of the cracked component. Since the problem is non-linear, the domain decomposition technique, combined with the Steklov-Poincaré pseudo-differential boundary operator, is used to obtain the sensitivity of the associated shape functional with respect to the nucleation of a small circular inclusion with different material property from the background. Then, the obtained topological derivatives are used to indicate the regions, where the controls should be positioned in order to solve the minimization problem we are dealing with. Finally, a numerical example is presented showing the applicability of the proposed methodology.
Źródło:
Control and Cybernetics; 2019, 48, 2; 307-323
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal control of a fractional-order enzyme kinetic model
Autorzy:
Al-Basir, F.
Elaiw, A. M.
Kesh, D.
Roy, P. K.
Powiązania:
https://bibliotekanauki.pl/articles/206336.pdf
Data publikacji:
2015
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
enzyme kinetics
cooperative phenomenon
fractional derivative
mathematical modeling
Hamiltonian
optimal control problem
Opis:
Enzymes play a significant role in controlling the characteristics of various chemical and biochemical reactions. They act as catalysts that increase the rate of reaction without undergoing any change in quantity. Enzymatic reactions occur through the active sites, which combine with the substrates to form intermediate complexes, subsequently leading to products. An enzyme having two active sites can show cooperative phenomena. Against this background, an enzyme-kinetic mathematical model is formulated using fractional order derivatives. Optimal control mechanism has been incorporated into the fractional-order model system to maximize the product output. Euler-Lagrange optimality conditions are derived for the FOCP (fractional order control problem) using maximum principle. Numerical iterative schemes have been developed to solve the fractional order optimal control problem through Matlab.
Źródło:
Control and Cybernetics; 2015, 44, 4; 443-461
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the robustness of the topological derivative for Helmholtz problems and applications
Autorzy:
Leugering, Günter
Novotny, Antonio André
Sokolowski, Jan
Powiązania:
https://bibliotekanauki.pl/articles/2183490.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
topological derivative
shape optimization
inverse problems
Helmholtz problem
numerical methods
complex variables
Opis:
We consider Helmholtz problems in two and three dimensions. The topological sensitivity of a given cost function J(uɛ) with respect to a small hole Bɛ around a given point x0ɛ ∈ Bɛ ⊂ Ω depends on various parameters, like the frequency k chosen or certain material parameters or even the shape parameters of the hole Bɛ. These parameters are either deliberately chosen in a certain range, as, e.g., the frequencies, or are known only up to some bounds. The problem arises as to whether one can obtain a uniform design using the topological gradient. We show that for 2-d and 3-d Helmholtz problems such a robust design is achievable.
Źródło:
Control and Cybernetics; 2022, 51, 2; 227--248
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Kuhn-Tucker type optimality conditions for some class of nonsmooth programming problems
Autorzy:
Śmietański, M. J.
Powiązania:
https://bibliotekanauki.pl/articles/206291.pdf
Data publikacji:
2003
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
pochodna Diniego
pochodna Clarka
wypukłość uogólniona
liniowość uogólniona
warunki konieczne i wystarczające optymalności
nonsmooth programming
Dini derivative
Clarke derivative
generalized convexity
generalized linearity
necessary and sufficient optimality conditions
Opis:
We consider two nonlinear programming problems with nonsmooth functions. The necessary and sufficient first order optimality conditions use the Dini and Clarke derivatives. However, the obtained Kuhn-Tucker conditions have a rather classical form. The sufficient conditions alone are obtained thanks to some properties of generalized convexity and generalized linearity of functions. The necessary and sufficient optimality conditions are given in the Lagrange form.
Źródło:
Control and Cybernetics; 2003, 32, 2; 361-376
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A new approach for simultaneous shape and topology optimization based on dynamic implicit surface function
Autorzy:
Guo, H.
Zhao, K.
Wang, M. Y.
Powiązania:
https://bibliotekanauki.pl/articles/970141.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optymalizacja topologiczna
pochodna topologiczna
topology optimization
implicit
surface function
topological derivative
level set
Opis:
In the present paper, a new approach for structural topology optimization based on dynamic implicit surface function (DISF) is proposed. DISF is used to describe the shape/topology of a structure, which is approximated in terms of the nodal values. Then, a relationship is established between the element stiffness and the values of the implicit surface function on its four nodes. In this way and with some non-local treatments of the design sensitivities, not only the shape derivative but also the topological derivative of the optimal design can be incorporated in the numerical algorithm in a unified way. Numerical experiments demonstrate that by employing this approach, the computational efforts associated with DISF (and level set) based algorithms can be diminished. Clear optimal topologies and smooth structural boundaries free from any sign of numerical instability can be obtained simultaneously and efficiently.
Źródło:
Control and Cybernetics; 2005, 34, 1; 255-282
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Viability and generalized differential quotients
Autorzy:
Girejko, E.
Bartosiewicz, Z.
Powiązania:
https://bibliotekanauki.pl/articles/970016.pdf
Data publikacji:
2006
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
viability
differential inclusion
generalized differential quotient (GDQ)
contingent derivative
Cellina continuous approximability (CCA)
Opis:
Necessary and sufficient conditions for a set-valued map K : R → Rn to be GDQ-differentiable are given. It is shown that K is GDQ differentiate at to if and only if it has a local multiselection that is Cellina continuously approximable and Lipschitz at to. It is also shown that any minimal GDQ of K at (to,yo) is a subset of the contingent derivative of K at (to,yo), evaluated at 1. Then this fact is used to prove a viability theorem that asserts existence of a solution to the initial value problem y(t) ∈ F(t, y(t)), with y(to) =yo, where F : Gr(K) → Rn is an orientor field (i.e. multivalued vector field) defined only on the graph of K and K : T → Rn is a time-varying constraint multifunction. One of the assumptions is GDQ differentiability of K.
Źródło:
Control and Cybernetics; 2006, 35, 4; 815-829
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Shape and topology optimization of distributed parameter systems
Autorzy:
Sokołowski, J.
Żochowski, A.
Powiązania:
https://bibliotekanauki.pl/articles/206802.pdf
Data publikacji:
2013
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
shape optimization
topological derivative
asymptotic analysis
singularly perturbed geometrical domains
asymptotic expansion of energ functional
Opis:
The energy functional for an elliptic boundary value problem in two spatial dimensions is considered. The variations of shape functional resulting from the small shape-topological domain perturbations with the holes and inclusions in elastic body are determined. The exact representation of solutions to the boundary value problem is exploited for the purposes of asymptotic analysis. To this end the perturbed solutions of the boundary value problem are Expressem as the minimizers of perturbed energy functionals. The proposed method of asymptotic analysis results in the double asymptotic expansions, with respect to the size of a hole and to the contrast parameter of an inclusion with respect to the matrix, of solutions to the boundary value problems as well as of the associated energy functional. The shape sensitivity analysis of the energy functional with respekt of the boundary variations of an inclusion is performed. The further asymptotic analysis allows for the limit passage with the size of inclusion to zero. In this way the topological derivative of the energy functional is obtained. The proposed analysis can be used in the shape and topology optimum design for elastic bodies governed by the stationary as well as by the time dependent elasticity boundary value problems in the framework of selfadjoint extensions of elliptic operators.
Źródło:
Control and Cybernetics; 2013, 42, 1; 217-226
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 21

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