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Wyświetlanie 1-15 z 16
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
Tytuł:
Characterization of the space of solutions of the membrane shell equation for arbitrary C[sup 11] midsurfaces
Autorzy:
Delfour, M.
Powiązania:
https://bibliotekanauki.pl/articles/206735.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
asymptotic shell models
membrane shell equation
shells
Opis:
A comprehensive convergence theory of dynamical thin shell models for the purposes of control theory relies heavily on a thorough analysis of the static model and the complete specification of the spaces of solutions of the asymptotic solution for general midsurfaces ranging from the plate to arbitrary C[sup 1,1] midsurfaces. In this paper the existence of solution to the membrane shell equation is studied in a bounded open connected domain [omega] (Lipschitzian when [omega] has a boundary [gamma]) in a C[sup 1,1] midsurface for homogeneous Neumann boundary conditions or homogeneous Dirichlet boundary conditions on a part [gamma,omikron] of [gamma]. It is proved that its tangential part is solution of the reduced membrane shell equation in H[sup 1](omega)[sup N] (resp. H[sup 1][sub gamma,omikron](omega)[sup N]) unique up to an element of a finite dimensional subspace, while its normal component belongs to a weighted L[sup 2](omega) space by the pointwise norm of the second fundamental form. It is also shown that the reduced equation is equivalent to the equation for the projection onto the linear subspace of vector functions whose linear change of metric tensor is orthogonal to the second fundamental form of the midsurface.
Źródło:
Control and Cybernetics; 1999, 28, 3; 481-501
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stability of nominally stable uncertain singularly perturbed systems with multiple time delays
Autorzy:
Chen, C.
Pan, S.
Hsieh, J.
Powiązania:
https://bibliotekanauki.pl/articles/206124.pdf
Data publikacji:
2002
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
stabilność asymptotyczna
asymptotic stability
delay-dependent criterion
singularly perturbed system
Opis:
In this paper, the robust asymptotic stability problem for a class of nominally stable uncertain singularly perturbed systems with multiple non-commensurate time delays is considered. A delay-dependent criterion is first proposed in this paper to guarantee robust asymptotic stability of the system under consideration. Based on this result, the range of allowable bounds of the perturbation matrices preserving the closed-loop stability can easily be found. Moreower, a simple criterion is also proposed to guarantee asymptotic, stability of the nominal system. Furthermore, a simple estimation of the stability bound epsilon* is proposed such that the nominal system is asymptotically stable for epsilon [belongs to](0,epsilon*). It can be seen that the stability bound proposed in this paper is less conservative than that presented in recent research. Finally, a numerical example is provided to illustrate our main results.
Źródło:
Control and Cybernetics; 2002, 31, 1; 5-16
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Topological sensitivity analysis for elliptic problems on graphs
Autorzy:
Leugering, G.
Sokolowski, J.
Powiązania:
https://bibliotekanauki.pl/articles/970307.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
differential equations on metric graphs
obstacles
topology optimization
asymptotic analysis
Opis:
We consider elliptic problems on graphs under given loads and bilateral contact conditions. We ask the question: which graph is best suited to sustain the loads and the constraints. More precisely, given a cost function we may look at a multiple node of the graph with edge degree q and ask as to whether that node should be resolved into a number of nodes of edge degree less than q, in order to decrease the cost. With this question in mind, we are looking into the sensitivity analysis of a graph carrying a second order elliptic equation with respect to changing its topology by releasing nodes with high edge degree or including an edge. With the machinery at hand developed here, we are in the position to define the topological gradient of an elliptic problem on a graph.
Źródło:
Control and Cybernetics; 2008, 37, 4; 971-997
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Adaptive finite elements based on sensitivities fortopological mesh changes
Autorzy:
Friederich, J.
Leugering, G.
Steinmann, P.
Powiązania:
https://bibliotekanauki.pl/articles/205694.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
adaptive mesh refinement
sensitivity-based refinement
topological sensitivity
asymptotic expansion
Opis:
We propose a novel approach to adaptive refinement in FEM based on local sensitivities for node insertion. To this end, we consider refinement as a continuous graph operation, for instance by splitting nodes along edges. Thereby, we introduce the concept of the topological mesh derivative for a given objective function. For its calculation, we rely on the first-order asymptotic expansion of the Galerkin solution of a symmetric linear second-order elliptic PDE. In this work, we apply this concept to the total potential energy, which is related to the approximation error in the energy norm. In fact, our approach yields local sensitivities for minimization of the energy error by refinement. Moreover, we prove that our indicator is equivalent to the classical explicit a posteriori error estimator in a certain sense. Numerical results suggest that our method leads to efficient and competitive adaptive refinement.
Źródło:
Control and Cybernetics; 2014, 43, 2; 279-306
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 the stability of continuous-time positive switched systems with rank one difference
Autorzy:
Fornasini, E.
Valcher, M. E.
Powiązania:
https://bibliotekanauki.pl/articles/971053.pdf
Data publikacji:
2013
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
switched system
positive linear system
asymptotic stability
linear copositive Lyapunov function quadratic Lyapunov function
Opis:
Continuous-time positive systems, switching among p subsystems whose matrices differ by a rank one matrix, are introduced, and a complete characterization of the existence of a common linear copositive Lyapunov function for all the subsystems is provided. Also, for this class of systems it is proved that a well-known necessary condition for asymptotic stability, namely the fact that All convex combinations of the system matrices are Hurwitz, becomes equivalent to the generally weaker condition that the systems matrices are Hurwitz. In the special case of two-dimensional systems, this allows for drawing a complete characterization of asymptotic stability. Finally, the case when there are only two subsystems, possibly with commuting matrices, is investigated.
Źródło:
Control and Cybernetics; 2013, 42, 1; 47-62
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Analysis of undamped second order systems with dynamic feedback
Autorzy:
Mitkowski, W.
Powiązania:
https://bibliotekanauki.pl/articles/970462.pdf
Data publikacji:
2004
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
stabilność asymptotyczna
stabilizacja ze sprzężeniem zwrotnym
sieć łańcuchowa
asymptotic stability
feedback stabilization
ladder network
Opis:
In this paper the stabilization problem of undamped second order system is considered. The stabilization by first order dynamic feedback is studied. The global asymptotic stability of the respectively closed-loop system is proved by LaSalle's theorem. As an example of application of the proposed method an electric ladder network L and Ic type is presented. Numerical calculations were made using the Matlab/Simulink program.
Źródło:
Control and Cybernetics; 2004, 33, 4; 563-572
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Influence of a boundary perforation on the Dirichlet energy
Autorzy:
Dambrine, M.
Vial, G.
Powiązania:
https://bibliotekanauki.pl/articles/970142.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
pochodna kształtu
pochodna topologiczna
singular shape perturbation
shape derivatives
topological derivatives
multi-scale asymptotic expansion
Opis:
We consider some singular perturbations of the boundary of a smooth domain. Such domain variations are not differentiable within the classical theory of shape calculus. We mimic the topological asymptotic and we derive an asymptotic expansion of the shape function in terms of a size parameter. The two-dimensional case of the Dirichlet energy is treated in detail. We give a full theoretical proof as well as a numerical confirmation of the results.
Źródło:
Control and Cybernetics; 2005, 34, 1; 117-136
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the choice of statistical model for one-dimensional P-algorithms
Autorzy:
Calvin, J.
Zilinskas, A.
Powiązania:
https://bibliotekanauki.pl/articles/205977.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
analiza statystyczna
model statystyczny
optymalizacja
prawdopodobieństwo
algorithm
asymptotic properties
convergence
optimization
probability
statistical analysis
statistical models
Opis:
Algorithms based on statistical models compete favorably with other global optimization algorithms as proved by extensive testing results. Recently, techniques were developed for theoretically estimating the rate of convergence of global optimization algorithms with respect to the underlying statistical models. In the present paper these technictues are extended for theoretical investigation of P-algorithms without respect to a statistical model. Theoretical estimates may eliminate the need for lengthy experimental investigation which previously was the only method for comparison of the algorithms. The rcaults obtained give new insight into the role of the mnderlying statistical model with respect to the asymptotic properties of the algorithm which will be useful for the implementation of new versions of the algoritlmns.
Źródło:
Control and Cybernetics; 2000, 29, 2; 555-565
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Representations of hypersurfaces and minimal smoothness of the midsurface in the theory of shells
Autorzy:
Delfour, M. C.
Powiązania:
https://bibliotekanauki.pl/articles/970297.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
thin shell
asymptotic shell
midsurface
smoothness
representation of a surface
oriented distance function
bi-Lipschitz mapping
tubular neighborhood
Opis:
Many hypersurfaces ω in R^N can be viewed as a subset of the boundary Γ of an open subset Ω of R^N. In such cases, the gradient and Hessian matrix of the associated oriented distance function ba to the underlying set Ω completely describe the normal and the N fundamental forms of ω, and a fairly complete intrinsic theory of Sobolev spaces on C1'1-hypersurfaces is available in Delfour (2000). In the theory of thin shells, the asymptotic model only depends on the choice of the constitutive law, the midsurface, and the space of solutions that properly handles the loading applied to the shell and the boundary conditions. A central issue is the minimal smoothness of the midsurface to still make sense of asymptotic membrane shell and bending equations without ad hoc mechanical or mathematical assumptions. This is possible for a C1'1-midsurface with or without boundary and without local maps, local bases, and Christoffel symbols via the purely intrinsic methods developed by Delfour and Zolesio (1995a) in 1992. Anicic, LeDret and Raoult (2004) introduced in 2004 a family of surfaces ω that are the image of a connected bounded open Lipschitzian domain in R² by a bi-Lipschitzian mapping with the assumption that the normal field is globally Lipschizian. >From this, they construct a tubular neighborhood of thickness 2h around the surface and show that for sufficiently small h the associated tubular neighborhood mapping is bi-Lipschitzian. We prove that such surfaces are C1'1-surfaces with a bounded measurable second fundamental form. We show that the tubular neighborhood can be completely described by the algebraic distance function to ω and that it is generally not a Lipschitzian domain in R³ by providing the example of a plate around a flat surface ω verifying all their assumptions. Therefore, the G1-join of K-regular patches in the sense of Le Dret (2004) generates a new K-regular patch that is a C1'1-surface and the join is C1'1. Finally, we generalize everything to hypersurfaces generated by a bi-Lipschitzian mapping defined on a domain with facets (e.g. for sphere, torus). We also give conditions for the decomposition of a C1'1-hypersurface into C1'1-patches.
Źródło:
Control and Cybernetics; 2008, 37, 4; 879-911
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Asymptotic analysis of three random branching walk models arising in molecular biology
Analiza asymptotyczna trzech modeli błądzenia z rozgałęzieniami z dziedziny biologii molekularnej
Autorzy:
Świerniak, A.
Polański, A.
Śmieja, J.
Kimmel, M.
Rzeszowska-Wolny, J.
Powiązania:
https://bibliotekanauki.pl/articles/206737.pdf
Data publikacji:
2003
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
analiza asymptotyczna
modelowanie biomatematyczne
procesy rozgałęzień
systemy nieskończenie wymiarowe
asymptotic analysis
biomathematical modelling
branching processes
infinite dimensional systems
Opis:
Using asymptotic techniques based on Laplace transforms, spectral analysis and theory of feedback systems, we characterise the asymptotic behaviour of the repeat loci in microsatellite DNA and cancer cells with increasing number of copies of genes responsible for coding proteins causing drug removal or metabolisation as well as telomeres shortening, which is supposed to be the mechanism of ageing and death. These three problems are described by models in the form of infinitely many differential linear or bilinear first order equations, resulting from branching random walk processes used to represent the evolution of particles in these problems.
Wykorzystując techniki asymptotyczne oparte na transformatach Laplace'a, analizę spektralną oraz teorię układów ze sprzężeniem zwrotnym w artykule scharakteryzowano zachowanie asymptotyczne powtórek w DNA mikrosatelitarnym oraz w komórkach rakowych z rosnącą liczbą kopii genów odpowiedzialnych za kodowanie białek powodujących usuwanie lub przemianę metaboliczną leków, a także skracanie telomerów, o którym się sądzi, że jest mechanizmem starzenia się i śmierci. Te trzy zagadnienia są opisywane przy pomocy modeli w postaci nieskończonej liczby liniowych lub biliniowych równań pierwszego rzędu, wynikających z procesów błądzenia, stosowanych do opisu ewolucji cząstek w tych zagadnieniach.
Źródło:
Control and Cybernetics; 2003, 32, 1; 147-162
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Jurdjevic-Quinn theorem for stochastic differential systems under weak conditions
Autorzy:
Florchinger, Patrick
Powiązania:
https://bibliotekanauki.pl/articles/2183489.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
stochastic differential system
weak solution of stochastic differential equation
asymptotic stability in probability
Barbashin–Krasovskii theorem
stabilizing state feedback law
Opis:
The purpose of this paper is to provide sufficient conditions for the stabilizability of weak solutions of stochastic dif- ferential systems when both the drift and diffusion are affine in the control. This result extends the well–known theorem of Jurdjevic–Quinn (Jurdjevic and Quinn, 1978) to stochastic differential systems under weaker conditions on the system coefficients than those assumed in Florchinger (2002).
Źródło:
Control and Cybernetics; 2022, 51, 1; 21--29
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Strong decay for one-dimensional wave equations with nonmonotone boundary damping
Autorzy:
Pierre, M.
Vancostenoble, J.
Powiązania:
https://bibliotekanauki.pl/articles/205904.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
równanie falowe
stabilność
asymptotic behavior
boundary control
d'Alembert formula
distribute parameter system
global existence
nonliner control system
nonmonotone feedback
stabilization
wave equation
Opis:
This paper is a contribution to the following question : consider the classical wave equation damped by a nonlinear feedback control which is only assumed to decrease the energy. Then, do solutions to the perturbed system still exist for all time? Does strong stability occur in the sense that the energy tends to zero as time tends to infinity? We prove here that the answer to both questions is positive in the specific case of the one-dimensional wave equation damped by boundary controls which are functions of the observed velocity. The main point is that no monotonicity assumption is made on the damping term.
Źródło:
Control and Cybernetics; 2000, 29, 2; 473-484
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Topological sensitivity analysis for a coupled nonlinear problem with an obstacle
Autorzy:
Abdelbari, M.
Nachi, K.
Sokolowski, J.
Powiązania:
https://bibliotekanauki.pl/articles/205653.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
topological derivative
shape optimization
SteklovPoincaroperator
Signorini problem
variational inequality
Helmholtz equation
coupled partial differential equations
conical differential
asymptotic expansions
singular perturbations of geometrical Romains
truncated domain
Opis:
The Topological Derivative has been recognized as a powerful tool in obtaining the optimal topology for several kinds of engineering problems. This derivative provides the sensitivity of the cost functional for a boundary value problem for nucleation of a small hole or a small inclusion at a given point of the domain of integration. In this paper, we present a topological asymptotic analysis with respect to the size of singular domain perturbation for a coupled nonlinear PDEs system with an obstacle on the boundary. The domain decomposition method, referring to the SteklovPoincar´epseudo-differential operator, is employed for the asymptotic study of boundary value problem with respect to the size of singular domain perturbation. The method is based on the observation that the known expansion of the energy functional in the ring coincides with the expansion of the Steklov-Poincar´e operator on the boundary of the truncated domain with respekt to the small parameter, which measures the size of perturbation. In this way, the singular perturbation of the domain is reduced to the regular perturbation of the Steklov-Poincar´e map ping for the ring. The topological derivative for a tracking type shape functional is evaluated so as to obtain the useful formula for application in the numerical methods of shape and topology optimization.
Źródło:
Control and Cybernetics; 2017, 46, 1; 5-25
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 16

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