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Tytuł:
The orders of the reductions of a point in the Mordell-Weil group of an elliptic curve
Autorzy:
Cheon, J.
Hahn, S.
Powiązania:
https://bibliotekanauki.pl/articles/1390534.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Bang's theorem
elliptic curves
reductions
local heights
Źródło:
Acta Arithmetica; 1999, 88, 3; 219-111
0065-1036
Pojawia się w:
Acta Arithmetica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Second order optimality conditions for bang-bang control problems
Autorzy:
Maurer, H.
Osmolovskii, N. P.
Powiązania:
https://bibliotekanauki.pl/articles/970524.pdf
Data publikacji:
2003
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowanie przekaźnikowe
bang-bang control
second order necessary and sufficient conditions
critical cone
transformation of quadratic forms
numerical verification of second order conditions
van der Pol oscillator
Opis:
Second order necessary and sufficient optimality conditions for bang-bang control problems have been studied in Milyutin, Osmolovskii (1998). These conditions amount to testing the positive (semi-)definiteness of a quadratic form on a critical cone. The assumptions are appropriate for numerical verification only in some special cases. In this paper, we study various transformations of the quadratic form and the critical cone which will be tailored to different types of control problems in practice. In particular, by means of a solution to a linear matrix differential equation, the quadratic form can be converted to perfect squares. We demonstrate by three practical examples that the conditions obtained can be verified numerically.
Źródło:
Control and Cybernetics; 2003, 32, 3; 555-584
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimality and sensitivity for semilinear bang-bang type optimal control problems
Autorzy:
Felgenhauer, U.
Powiązania:
https://bibliotekanauki.pl/articles/907953.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
sterowanie optymalne
struktura roztworu
warunki optymalności
bang-bang control
optimality conditions
sensitivity differentials
solution structure
stability in optimal control
strong local optima
Opis:
In optimal control problems with quadratic terminal cost functionals and systems dynamics linear with respect to control, the solution often has a bang-bang character. Our aim is to investigate structural solution stability when the problem data are subject to perturbations. Throughout the paper, we assume that the problem has a (possibly local) optimum such that the control is piecewise constant and almost everywhere takes extremal values. The points of discontinuity are the switching points. In particular, we will exclude the so-called singular control arcs, see Assumptions 1 and 2, Section 2. It is known from the results by Agrachev et al. (2002) stating that regularity assumptions, together with a certain strict second-order condition for the optimization problem formulated in switching points, are sufficient for strong local optimality of a state-control solution pair. This finite-dimensional problem is analyzed in Section 3 and optimality conditions are formulated (Lemma 2). Using well-known results concerning solution sensitivity for mathematical programs in Rn (Fiacco, 1983) one may further conclude that, under parameter changes in the problem data, the switching points will change Lipschitz continuously. The last section completes these qualitative statements by calculating sensitivity differentials (Theorem 2, Lemma 6). The method requires a simultaneous solution of certain linearized multipoint boundary value problems.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2004, 14, 4; 447-454
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Bang-bang controls in the singular perturbations limit
Autorzy:
Artstein, Z.
Powiązania:
https://bibliotekanauki.pl/articles/970546.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
zaburzenia osobliwe
miara Younga
bang-bang
singular perturbations
Young measures
Opis:
A general form of the dynamics obtained as a limit of trajectories of singularly perturbed linear control systems is presented. The limit trajectories are described in terms of probability measure-valued maps. This allows to determine the extent to which the bang-bang principle for linear control systems is carried over to the singular limit.
Źródło:
Control and Cybernetics; 2005, 34, 3; 645-663
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Equivalence of second order optimality conditions for bang-bang control problems. Part 1: Main results
Autorzy:
Osmolovskii, N. P.
Maurer, H.
Powiązania:
https://bibliotekanauki.pl/articles/970559.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sterowanie przekaźnikowe
stożek krytyczny
forma kwadratowa i równoważność
bang-bang control
second order necessary and sufficient conditions
critical cone
Opis:
Second order optimality conditions have been derived in the literature in two different forms. Osmolovskii (1988a, 1995, 2000, 2004) obtained second order necessary and sufficient conditions requiring that, a certain quadratic form be positive (semi)-definite on a critical cone. Agrachev, Stefani, Zezza (2002) first, reduced the bang-bang control problem to finite-dimensional optimization and then show that well-known sufficient optimality conditions for this optimization problem supplemented by the strict bang-bang property furnish sufficient conditions for the bang-bang control problem. In this paper, we establish the equivalence of both forms of sufficient conditions and give explicit relations between corresponding Lagrange multipliers and elements of critical cones. Part 1 summarizes the main results while detailed proofs will be given in Part 2.
Źródło:
Control and Cybernetics; 2005, 34, 3; 927-950
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimality properties of controls with bang-bang components in problems with semilinear state equation
Autorzy:
Felgenhauer, U.
Powiązania:
https://bibliotekanauki.pl/articles/970553.pdf
Data publikacji:
2005
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
warunki optymalności
równanie Riccatiego
sterowanie przekaźnikowe
czułość
optimality conditions
Riccati equation
bang-bang control
switching points optimization
sensitivity
Opis:
In this paper we study optimal control problems with bang-bang solution behavior for a special class of semilinear dynamics. Generalizing a former result for linear systems, optimlity conditions are derived by a duality based approach. The results apply for scalar as well as for vector control functions and, in particular, for the case of the so-called multiple switches, too. Further, an iterative procedure for determining switching points is proposed, and convergence results are provided.
Źródło:
Control and Cybernetics; 2005, 34, 3; 763-785
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Equivalence of second order optimality conditions for bang-bang control problems. Part 2 : Proofs, variational derivatives and representations
Autorzy:
Osmolovskii, N. P.
Maurer, H.
Powiązania:
https://bibliotekanauki.pl/articles/969736.pdf
Data publikacji:
2007
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
bang-bang control
second order necessary and sufficient conditions
critical cones
equivalence of quadratic forms
representation of the Hessian of the Lagrangian
Opis:
In Part 1 of this paper (Osmolovskii and Maurer, 2005), we have summarized the main results on the equivalence of two quadratic forms from which second order necessary and sufficient conditions can be derived for optimal bang-bang control problems. Here, in Part 2, we give detailed proofs and elaborate explicit relations between Lagrange multipliers and elements of the critical cones in both approaches. The main analysis concerns the derivation of formulas for the first and second order derivatives of trajectories with respect to variations of switching times, initial and final time and initial point. This leads to explicit representations of the second order derivatives of the Lagrangian for the induced optimization problem. Based on a suitable transformation, we obtain the elements of the Hessian of the Lagrangian in a form which involves only first order variations of the nominal trajectory. Finally, a careful regrouping of all terms allows us to find the desired equivalence of the two quadratic forms.
Źródło:
Control and Cybernetics; 2007, 36, 1; 5-45
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Sufficient optimality conditions for a bang-singular extremal in the minimum time problem
Autorzy:
Poggiolini, L.
Stefani, G.
Powiązania:
https://bibliotekanauki.pl/articles/969613.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
minimum time
second order sufficient conditions
bang-singular arc
Hamiltonian formalism
Opis:
The paper gives second order sufficient conditions for the strong local optimality of a bang-singular extremal in a minimum time problem. The conditions are given in terms of regularity assumptions on the extremal and of the coercivity of the extended second variation associated to the minimum time problem with fixed end-points on the singular arc. The conditions are close to the necessary ones in the usual sense, namely we require strict inequalities where necessary conditions have mild inequalities.
Źródło:
Control and Cybernetics; 2008, 37, 2; 469-490
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Teologia naturalna Sir Edmunda Tylora Whittakera
Natural theology of Sir Edmund Tylor Whittaker
Autorzy:
Pabjan, Tadeusz
Powiązania:
https://bibliotekanauki.pl/articles/690594.pdf
Data publikacji:
2008
Wydawca:
Copernicus Center Press
Tematy:
Edmund Whittaker
natural theology
Big Bang
creation 'ex nihilo'
philosophy of mathematics
cosmology
determinism
free will
Opis:
There were scientists who believed that the beginning of the universe that cosmology speaks about should be identified with the moment of creation by God. One of them was Edmund Whittaker, who was convinced that the Big Bang provides a kind of scientific proof of the creation 'ex nihilo' and consequently of the existence of God. The present paper gives a short account of his natural theology. In the first chapter, Whittaker's philosophy of mathematics is presented - this is his point of departure: rational and mathematical character of the world is - in his opinion - a source of our knowledge of God. Chapters two and three give an account of Whittaker's natural theology; the stress is put on the Big Bang as a moment of the world's creation. In chapter four, the relevance of cosmology for the understanding of the Five Ways to God of St. Thomas is discussed. The last chapter deals with the problem of determinism and free will as seen by Edmund Whittaker.
Źródło:
Zagadnienia Filozoficzne w Nauce; 2008, 42; 78-111
0867-8286
2451-0602
Pojawia się w:
Zagadnienia Filozoficzne w Nauce
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The shooting approach in analyzing bang-bang extremals with simultaneous control switches
Autorzy:
Felgenhauer, U.
Powiązania:
https://bibliotekanauki.pl/articles/969603.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
bang-bang control
Lipschitz stability in optimal control
nonsmooth optimization
shooting type methods
Opis:
The paper is devoted to stability investigation of optimal structure and switching points position for parametric bang-bang control problem with special focus on simultaneous switches of two control components. In contrast to problems where only simple switches occur, the switching points in general are no longer differentiable functions of input parameters. Conditions for Lipschitz stability are found which generalize known sufficient optimality conditions to nonsmooth situation. The analysis makes use of backward shooting representation of extremals, and of generalized implicit function theorems. The Lipschitz properties are illustrated for an example by constructing backward parameterized family of extremals and providing first-order switching points prediction.
Źródło:
Control and Cybernetics; 2008, 37, 2; 307-327
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimality and stability result for bang-bang optimal controls with simple and double switch behaviour
Autorzy:
Felgenhauer, U.
Poggiolini, L.
Stefani, G.
Powiązania:
https://bibliotekanauki.pl/articles/970776.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
bang-bang control
parametric control problems
Hamiltonian flows
Opis:
The paper considers parametric optimal control problems with bang-bang control vector function. For this problem we give regularity and second-order optimality conditions at the nominal solution which are sufficient to: (i) existence and local uniqueness of extremals, (ii) local structure stability, (iii) strong local optimality, under parameter perturbations. Here "local" means in a L∞ neighbourhood of the nominal trajectory, regardless of the control values. Stability results were obtained by the first author using the shooting approach, while optimality results were obtained by the other authors, using the Hamiltonian approach. The paper, combining both approaches, allows to unify the assumptions and to close some gaps between optimality and stability results.
Źródło:
Control and Cybernetics; 2009, 38, 4B; 1305-1325
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Application of Digital Control Techniques for Satellite Medium Power DC-DC Converters
Autorzy:
Skup, K. R.
Grudziński, P.
Orleański, P.
Powiązania:
https://bibliotekanauki.pl/articles/226506.pdf
Data publikacji:
2011
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
DC-DC switching converter
digital feedback loop
FPGA
VHDL
digital current mode control
digital voltage
regulator
bang-bang control
digital PID
PWM
Opis:
The objective of this paper is to present a work concerning a digital control loop system for satellite medium power DC-DC converters that is done in Space Research Centre. The whole control process of a described power converter is based on a high speed digital signal processing. The paper presents a development of a FPGA digital controller for voltage and current mode stabilization that was implemented using VHDL. The described controllers are based on a classical digital PID controller. The converter used for testing is a 200 kHz, 750W buck converter with 50V/15A output. A high resolution digital PWM approach is presented. Additionally a simple and effective solution of filtering of an analog-to-digital converter output is presented.
Źródło:
International Journal of Electronics and Telecommunications; 2011, 57, 1; 77-83
2300-1933
Pojawia się w:
International Journal of Electronics and Telecommunications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Regularization and discretization of linear-quadratic control problems
Autorzy:
Alt, W.
Seydenschwanz, M.
Powiązania:
https://bibliotekanauki.pl/articles/206162.pdf
Data publikacji:
2011
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
bang-bang control
regularization
discretization
Opis:
We analyze regularizations of a class of linear-quadratic optimal control problems with control appearing linearly. It is shown that if the optimal control is bang-bang or if a coercivity condition for the state variables is satisfied, the solutions are continuous functions of the regularization parameter. Combining error estimates for Euler discretizations of the regularized problems with those for the regularization error, we choose the regularization parameter in dependence of the meshsize to obtain optimal convergence rates for the discrete solutions. Numerical experiments confirm the theoretical findings.
Źródło:
Control and Cybernetics; 2011, 40, 4; 903-920
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
W. Bang’s note on MF 18, 25 ff
Autorzy:
Knüppel, Michael
Powiązania:
https://bibliotekanauki.pl/articles/634669.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Jagielloński. Wydawnictwo Uniwersytetu Jagiellońskiego
Tematy:
Willy Bang, Edward Schröder, German studies, archive materials, history of linguistics
Opis:
The following short article deals with an unpublished comment W. Bang wrote on a passage from “Des Minnesangs Frühling”. Bang was sending this short note for a journal edited by E. Schröder who used it for his own comment of the same passage but without referring to Bang.
Źródło:
Studia Linguistica Universitatis Iagellonicae Cracoviensis; 2011, 128
2083-4624
Pojawia się w:
Studia Linguistica Universitatis Iagellonicae Cracoviensis
Dostawca treści:
Biblioteka Nauki
Artykuł
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