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Wyświetlanie 1-15 z 47
Tytuł:
Hamiltonian form of the maximum principle
Autorzy:
Gamkrelidze, R. V.
Powiązania:
https://bibliotekanauki.pl/articles/970916.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
Pontryagin's maximum principle
Hamiltonian form of the maximum principle
Opis:
According to the goal of the Conference in Bedlewo, dedicated to the 50-th anniversary of Optimal Control theory, and considering that the 2008 year marked the centennial birthday of Lev Semenovich Pontryagin, I decided to devote my talk to a brief account on the discovery of the maximum principle and to an analysis of its basic feature, the Hamiltonian format.
Źródło:
Control and Cybernetics; 2009, 38, 4A; 959-971
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A simple proof of the maximum principle with endpoint constraints
Autorzy:
Korytowski, A.
Powiązania:
https://bibliotekanauki.pl/articles/205969.pdf
Data publikacji:
2014
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
maximum principle
Opis:
The paper presents a new, relatively simple proof of Pontryagin’s maximum principle for the canonical problem of optimal control, with equality and inequality constraints imposed on the trajectory endpoints. The proof combines together two ideas, which appeared separately in the earlier works: application of the Karush-John conditions for finite-dimensional problems, and using packages of needle variations.
Źródło:
Control and Cybernetics; 2014, 43, 1; 5-13
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Maximum Principle of optimal control: A history of ingenious ideas and missed opportunities
Autorzy:
Pesch, H. J.
Plail, M.
Powiązania:
https://bibliotekanauki.pl/articles/970918.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
history of optimal control
maximum principle
Opis:
On the occasion of (more than) 50 years of optimal control theory, this paper deals with the development of the maximum principle of optimal control during the early times of the Cold War, when mathematicians in the US and the USSR made every endeavor to solve minimum time interception problems, which later on became prototypes of the first optimal control problems. The paper is a short survey on the history of optimal control, a sequence of ingenious ideas and regrets of missed opportunities. The conclusions of the paper are extracted from the second author's monograph on the development of optimal control theory from its commencements until it became an independent discipline in mathematics. The present paper also includes secondary literature published thereafter.
Źródło:
Control and Cybernetics; 2009, 38, 4A; 973-995
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Sformułowanie problemu optymalnego kształtowania wielogałęziowych ustrojów prętowych w kategoriach teorii sterowania
Formulating the problem of shaping multi-branch bar arrangements in the optimum manner in terms of the control theory
Autorzy:
Laskowski, H.
Powiązania:
https://bibliotekanauki.pl/articles/154412.pdf
Data publikacji:
2012
Wydawca:
Stowarzyszenie Inżynierów i Techników Mechaników Polskich
Tematy:
optymalizacja
zasada maksimum
optimization
maximum principle
Opis:
W artykule przedstawiono oryginalną metodę formułowania zadań optymalizacji wielogałęziowych ustrojów prętowych, polegającą na dekompozycji ustroju na pojedyncze pręty, sformułowaniu warunków współpracy oraz normalizacji ich długości. Wykazano, że zaprezentowana metoda umożliwia, w odniesieniu do ustrojów wielogałęziowych, formułowanie zadań optymalizacji w kategoriach teorii sterowania. Opisaną metodę zastosowano w optymalizacji przykładowego ustroju słupowo ryglowego złożonego z pięciu prętów.
The paper presents an original method for formulating problems of optimization of multi-branch bar arrangements which consists in decomposing them into single bars, formulating their cooperation conditions, and normalizing their lengths. In Section 2 there is defined the concept of multi-branch arrangements, which has not occurred in the literature so far. The next section presents ways for describing bars with special attention being paid to the rules of formulating their cooperation conditions. Sections 4 and 5 are devoted to description of the decomposition and normalization method, which can be used to formulate the problem of optimization of multi-branch bar arrangements in the form of a double-point boundary problem, whose formal structure makes it possible to use the maximum principle. The above method was used to optimize an example bar-and-beam arrangement consisting of five bars, which is discussed in Section 6. With reference to the analyzed object subjected to three fundamental load conditions in three combinations, a problem of shaping its cross-section in the optimum manner was formulated. There was assumed the optimization problem objective function as the steel volume. Five decision variables were assumed to be I-beam web heights. There were also taken into account restrictions of the optimization problem resulting from the bar load-carrying ability and usability limits. Eventually, a double-point boundary problem was formulated consisting of 197 differential and algebraic equations, which was solved using the Dircol-2.1 software.
Źródło:
Pomiary Automatyka Kontrola; 2012, R. 58, nr 10, 10; 887-891
0032-4140
Pojawia się w:
Pomiary Automatyka Kontrola
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Pontryagin Maximum Principle for coupled slow and fast systems
Autorzy:
Artstein, Z.
Powiązania:
https://bibliotekanauki.pl/articles/970920.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
singular perturbations
maximum principle
Opis:
When slow and fast controlled dynamics are coupled, the variational limit, as the ratio of time scales grows, is best depicted as a trajectory in a probability measures space. The effective control is then an invariant measure on the fast state-control space. The paper presents the form of the Pontryagin Maximum Principle for this variational limit and examines its relation to the Maximum Principle of the perturbed system.
Źródło:
Control and Cybernetics; 2009, 38, 4A; 1003-1019
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The maximum principle for viscosity solutions of elliptic differential functional equations
Autorzy:
Karpowicz, A.
Powiązania:
https://bibliotekanauki.pl/articles/254694.pdf
Data publikacji:
2013
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
maximum principle
viscosity solution
elliptic equations
Opis:
This paper is devoted to the study of the maximum principle for the elliptic equation with a deviated argument. We will consider viscosity solutions of this equation.
Źródło:
Opuscula Mathematica; 2013, 33, 1; 99-105
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The nonsmooth maximum principle
Autorzy:
Clarke, F. H.
Pinho, M. R. de
Powiązania:
https://bibliotekanauki.pl/articles/970885.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
Pontryagin maximum principle
nonsmooth analysis
Opis:
We present a brief survey of the nonsmooth maximum principle of optimal control, focusing, in particular, upon the alternative forms of the adjoint equation. We obtain a new version of the theorem that asserts for the first time the full Weierstrass condition together with the Euler form of the adjoint equation, thereby extending a result of de Pinho and Vinter. The new theorem also features stratified hypotheses and conclusions. Two examples illustrate its use.
Źródło:
Control and Cybernetics; 2009, 38, 4A; 1151-1167
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optymalne stopy inwestycji w N-kapitałowym modelu wzrostu gospodarczego
Optimal Investment Rates in an N-Capital Growth Model
Autorzy:
Tokarski, Tomasz
Powiązania:
https://bibliotekanauki.pl/articles/574446.pdf
Data publikacji:
2007-09-30
Wydawca:
Szkoła Główna Handlowa w Warszawie. Kolegium Analiz Ekonomicznych
Tematy:
investment rates
growth model
Pontryagin’s maximum principle
Opis:
The paper aims to determine an optimal structure of investment rates under an N-capital growth model. This model is a combination and expansion of models developed by Solow [1956]; Mankiw, Romer, Weil [1992]; Nonneman, Vanhoudt [1996]; and Tokarski [1996; 2000; 2003; 2005], with elements of optimal control models by Ramsey [1928], Lucas [1988] and Romer [1986, 1990]. The economic growth model described in the paper is based on the following assumptions: - The stream of products generated in the economy is influenced by a finite N amount of capital, labor and technology resources; it is also assumed that labor and technology resources grow according to certain exogenous growth rates; - The increase of each of the analyzed capital stocks is the difference between investment in this capital and its depreciation; these assumptions refer to the neoclassical growth models developed by Solow, Mankiw-Romer-Weil, and Nonneman-Vanhoudt; - A typical rationally behaving consumer (much as in the case of endogenous growth models developed by Lucas and Romer) seeks a long-term investment rate structure that will maximize the usefulness of consumption in an infinite period of time; - Additionally, an assumption is made that the macroeconomic production function in the described growth model does not have to be characterized by a constant scale effect (as earlier noted by Tokarski [1996, 2003 or 2005]). The model described by the author is solved using Pontryagin’s maximum principle.
Źródło:
Gospodarka Narodowa. The Polish Journal of Economics; 2007, 218, 9; 1-18
2300-5238
Pojawia się w:
Gospodarka Narodowa. The Polish Journal of Economics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Positive solutions of nonlinear elliptic systems
Autorzy:
Dalmasso, Robert
Powiązania:
https://bibliotekanauki.pl/articles/1311841.pdf
Data publikacji:
1993
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
a priori bounds
nonlinear elliptic systems
Maximum Principle
Opis:
We study the existence and nonexistence of positive solutions of nonlinear elliptic systems in an annulus with Dirichlet boundary conditions. In particular, $L^∞$ a priori bounds are obtained. We also study a general multiple linear eigenvalue problem on a bounded domain.
Źródło:
Annales Polonici Mathematici; 1993, 58, 2; 201-212
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Application of maximum principle to optimization of production and storage costs
Autorzy:
Popescu, Liviu
Dimitrov, Ramona
Powiązania:
https://bibliotekanauki.pl/articles/2083467.pdf
Data publikacji:
2021
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
optimal control
Pontryagin Maximum Principle
controllability
production
storage
Opis:
A problem of optimization for production and storge costs is studied. The problem consists in manufacture of n types of products, with some given restrictions, so that the total production and storage costs are minimal. The mathematical model is built using the framework of driftless control affine systems. Controllability is studied using Lie geometric methods and the optimal solution is obtained with Pontryagin Maximum Principle. It is proved that the economical system is not controllable, in the sense that we can only produce a certain quantity of products. Finally, some numerical examples are given with graphical representation.
Źródło:
Archives of Control Sciences; 2021, 31, 4; 865-881
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Global existence for strong solutions of viscous Burgers equation. (1) The bounded case
Autorzy:
Unterberger, J.
Powiązania:
https://bibliotekanauki.pl/articles/206077.pdf
Data publikacji:
2017
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
viscous Burgers equation
conservation laws
maximum principle
Schauder estimates
Opis:
We prove that the viscous Burgers equation (∂t−∆)u(t, x)+( u •∇)u(t, x) = g(t, x), (t, x) ∈ R+ × Rd (d ≥ 1) has a globally defined smooth solution in all dimensions provided the initial condition and the forcing term g are smooth and bounded together with their derivatives. Such solutions may have infinite energy. The proofdoes not rely on energy estimates, but on a combinationof the maximumprinciple and quantitative Schauder estimates. We obtain precise bounds on the sup norm of the solution and its derivatives, making it plain that there is no exponential increase in time. In particular, these bounds are time-independent if g is zero. To get a classical solution, it suffices to assume that the initial condition and the forcing term have bounded derivatives up to order two.
Źródło:
Control and Cybernetics; 2017, 46, 2; 109-136
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Strong maximum principles for infinite systems of parabolic differential-functional inequalities with initial constant estimates
Autorzy:
Brandys, Jolanta
Powiązania:
https://bibliotekanauki.pl/articles/745310.pdf
Data publikacji:
2007
Wydawca:
Polskie Towarzystwo Matematyczne
Tematy:
infinite systems
parabolic differential-functional inequalities
strong maximum principle
Opis:
The purpose of this paper is to present strong maximum principles for infinite systems of parabolic differential-functional inequalities with initial inequalities in relatively arbitrary \((n+1)\)-dimensional time-space sets more general than the cylindrical domain.
Źródło:
Commentationes Mathematicae; 2007, 47, 2
0373-8299
Pojawia się w:
Commentationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Growth of a polynomial not vanishing in a disk
Autorzy:
Mir, Abdullah
Powiązania:
https://bibliotekanauki.pl/articles/2078964.pdf
Data publikacji:
2019
Wydawca:
Uniwersytet Marii Curie-Skłodowskiej. Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
Tematy:
Polynomial
maximum modulus principle
zeros
Opis:
This paper deals with the problem of finding some upper bound estimates for the maximum modulus of the derivative and higher order derivatives of a complex polynomial on a disk under the assumption that the polynomial has no zeros in another disk. The estimates obtained strengthen the well-known inequality of Ankeny and Rivlin about polynomials.
Źródło:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica; 2019, 73, 1; 41-48
0365-1029
2083-7402
Pojawia się w:
Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A simple trolley-like model in the presence of a nonlinear friction and a bounded fuel expenditure
Autorzy:
Dmitruk, Andrei
Samylovskiy, Ivan
Powiązania:
https://bibliotekanauki.pl/articles/729308.pdf
Data publikacji:
2013
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
optimal control problem
Pontryagin Maximum Principle
extremals
singular arcs
Opis:
We consider a problem of maximization of the distance traveled by a material point in the presence of a nonlinear friction under a bounded thrust and fuel expenditure. Using the maximum principle we obtain the form of optimal control and establish conditions under which it contains a singular subarc. This problem seems to be the simplest one having a mechanical sense in which singular subarcs appear in a nontrivial way.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2013, 33, 2; 135-147
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Normality of the maximum principle for absolutely continuous solutions to Bolza problems under state constraints
Autorzy:
Frankowska, H.
Powiązania:
https://bibliotekanauki.pl/articles/970777.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
optimal control
maximum principle under state constraints
normal necessary conditions
Opis:
It is well known that for a Bolza optimal control problem under state constraints every local minimizer satisfies a constrained maximum principle which may be degenerate. In the recent years several researchers proposed sufficient conditions for its nondegeneracy, e.g. Arutyanov and Assev (1997), Rampazzo and Vinter (1999, 2000), Galbraith and Vinter (2003). In all these papers the most important assumption links dynamics of a control system with tangent cones to constraints. It is the so called inward pointing condition of control theory that is in the same spirit with the well known Slater and Managasarian-Fromowitz conditions of mathematical programming. We propose here two sufficient conditions for normality when the boundary of constraints is C1 and the end point is free. The first one applies to every nondegenerate maximum principle without any assumptions on the initial state. The second one applies to every maximum principle, but involves an additional assumption on the initial conditions.
Źródło:
Control and Cybernetics; 2009, 38, 4B; 1327-1340
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 47

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