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Tytuł:
Theconjugate points sufficient conditions for an optimal control
Autorzy:
Szymanowska, A.
Powiązania:
https://bibliotekanauki.pl/articles/206818.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
pola ekstremali
problem Bolza
sterowanie optymalne
warunek wystarczający
field of extremals
generalized problem of Bolza
sufficient conditions
Opis:
The paper concerns an application of the idea of field theory and the concept of "concourse of flights" to the sufficient optimality conditions for the optimal control problems stated in terms of focal and conjugate points. The concept of concourse of flights was begun by Young (1969), and later extended by Nowakowski (1988). In the paper the definition of a focal and conjugate point of a field of extremals is given. Using these concepts, we prove that the existence of a field of extremals without conjugate points implies the existence of concourse of flights and consequently we obtain the second order sufficient conditions for the generalized problem of Bolza. Another approach to the concept of focal and conjugate points is given by Zeidan (1983, 1984).
Źródło:
Control and Cybernetics; 1998, 27, 3; 353-362
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The $p$-Factor Method for Nonlinear Optimization
Autorzy:
Szczepanik, Ewa
Prusińska, Agnieszka
Tret’yakov, Alexey
Powiązania:
https://bibliotekanauki.pl/articles/1373566.pdf
Data publikacji:
2012
Wydawca:
Uniwersytet Jagielloński. Wydawnictwo Uniwersytetu Jagiellońskiego
Tematy:
nonlinear optimization
kernel
singularity
convergence
necessary and sufficient conditions
$p$-factor operator
$p$-regularity
Opis:
We present the main concept and results of the $p$-regularity theory (also known as $p$-factor analysis of nonlinear mappings) applied to nonlinear optimization problems. The approach is based on the construction of $p$-factor operator. The main result of this theory gives a detailed description of the structure of the zero set of irregular nonlinear mappings. Applications include a new numerical method for solving nonlinear optimization problems and $p$-order necessary and sufficient optimality conditions. We substantiate the rate of convergence of $p$-factor method.
Źródło:
Schedae Informaticae; 2012, 21; 141-157
0860-0295
2083-8476
Pojawia się w:
Schedae Informaticae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal Control for a Class of Compartmental Models in Cancer Chemotherapy
Autorzy:
Świerniak, A.
Ledzewicz, U.
Schättler, H.
Powiązania:
https://bibliotekanauki.pl/articles/908158.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
medycyna
matematyka
compartmental models
cancer chemotherapy
optimal control
necessary and sufficient conditions for optimality
Opis:
We consider a general class of mathematical models P for cancer chemotherapy described as optimal control problems over a fixed horizon with dynamics given by a bilinear system and an objective which is linear in the control. Several two- and three-compartment models considered earlier fall into this class. While a killing agent which is active during cell division constitutes the only control considered in the two-compartment model, Model A, also two three-compartment models, Models B and C, are analyzed, which consider a blocking agent and a recruiting agent, respectively. In Model B a blocking agent which slows down cell growth during the synthesis allowing in consequence the synchronization of the neoplastic population is added. In Model C the recruitment of dormant cells from the quiescent phase to enable their efficient treatment by a cytotoxic drug is included. In all models the cumulative effect of the killing agent is used to model the negative effect of the treatment on healthy cells. For each model it is shown that singular controls are not optimal. Then sharp necessary and sufficient optimality conditions for bang-bang controls are given for the general class of models P and illustrated with numerical examples.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2003, 13, 3; 357-368
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Minima in control problems with constraints
Autorzy:
Stefani, Gianna
Zezza, PierLuigi
Powiązania:
https://bibliotekanauki.pl/articles/1359682.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
state-control constraint
necessary
second order conditions
conjugate points
optimal control
sufficient conditions
Opis:
This paper is devoted to describing second order conditions in the framework of extremal problems, that is, conditions obtained by reducing the optimal control problem to an abstract one in a suitable Banach (or Hilbert) space. The studied problem includes equality constraints both on the end-points and on the state-control trajectory. The second goal is to give a complete description of necessary and sufficient second order conditions for weak local optimality by describing first the associated linear-quadratic problem and then by giving a conjugate point theory for this linear quadratic problem with constraints.
Źródło:
Banach Center Publications; 1995, 32, 1; 361-378
0137-6934
Pojawia się w:
Banach Center Publications
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:
System of production order verification in application to service of customer
Autorzy:
Saniuk, A.
Saniuk, S.
Powiązania:
https://bibliotekanauki.pl/articles/118055.pdf
Data publikacji:
2005
Wydawca:
Polskie Towarzystwo Promocji Wiedzy
Tematy:
production order
sufficient conditions
production cost
Opis:
In this paper the efficiency of the System of Production Order Verification in application to service of customer is examined. Its aim is to find out whether a given work order can be accepted to be processed in an enterprise and satisfy the customer’s requirements within constraints imposed by the enterprise configuration and the process of manufacturing of other products. The presented system is illustrated on an example.
Źródło:
Applied Computer Science; 2005, 1, 1; 133-140
1895-3735
Pojawia się w:
Applied Computer Science
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:
Duality theory for state-constrained control problems governed by a first order PDE system
Autorzy:
Pickenhain, S.
Powiązania:
https://bibliotekanauki.pl/articles/205959.pdf
Data publikacji:
2002
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
teoria dwoistości
control problems with multiple integrals
duality theory
necessary and sufficient optimality conditions
Opis:
In this paper we prove weak and strong duality results for optimal control problems with multiple integrals, first-order partial differential equations and state constraints. We formulate conditions under which the sequence of canonical variables [y^epsilon] in the [epsilon]-maximum principle, proved in Pickenhain and Wagner (2000), form a maximizing sequence in the dual problem.
Źródło:
Control and Cybernetics; 2002, 31, 3; 833-845
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:
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:
Second order conditions in optimal control problems with mixed equality-type constraints on a variable time interval
Autorzy:
Osmolovskii, N. P.
Powiązania:
https://bibliotekanauki.pl/articles/970741.pdf
Data publikacji:
2009
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
piecewise continuous control
maximum principle
second order necessary or sufficient conditions
critical cone
quadratic form
Opis:
This paper provides an analysis of second-order necessary or sufficient optimality conditions of Pontryagin or bounded strong minima, for optimal control problems of ordinary differential equations, considered on a nonfixed time interval, with constraints on initial-final time-state as well as mixed state-control constraints of equality type satisfying condition of linear independence of gradients w.r.t. control.
Źródło:
Control and Cybernetics; 2009, 38, 4B; 1535-1556
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Shape optimization of control problems described by wave equations
Autorzy:
Nowakowski, A.
Powiązania:
https://bibliotekanauki.pl/articles/970316.pdf
Data publikacji:
2008
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
sufficient optimality conditions
control with wave equation
shape optimization
dual dynamic programming
Opis:
The control problem with multidimensional integral functional under wave type constraints for control is considered. Next a type of deformation with control of the domain is described and then we define suitable shape functional. Having denned trajectory and control of deformation dual dynamic programming tools are applied to derive optimality condition for the shape functional with respect to that deformation.
Źródło:
Control and Cybernetics; 2008, 37, 4; 1045-1055
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Dual sufficient optimality conditions for optimal control
Autorzy:
Młynarska, E.
Powiązania:
https://bibliotekanauki.pl/articles/205961.pdf
Data publikacji:
2001
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
minimum względne
nierówność podwójna Hamiltona-Jacobiego
zagadnienie sterowania optymalnego
dual Hamilton-Jacobi inequality
dual sufficient optimality conditions
optimal control problem
relative minimum
Opis:
In this paper we develop the first and second order dual sufficient optimality conditions for a nonlinear optimal control problem. Our conditions are derived from the dual Hamilton-Jacobi approach applied to the generalized problem of Bolza. We do not require neither any convexity on the data, nor that the control set U be polyhedral, nor that the control function be in the interior of U. Instead, we assume the existence of a function which satisfies a certain inequality.
Źródło:
Control and Cybernetics; 2001, 30, 1; 45-54
0324-8569
Pojawia się w:
Control and Cybernetics
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:
Analysis of pandemic with game methodology and numerical approximation
Autorzy:
Matusik, Radosław
Nowakowski, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/29432416.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
COVID-19
game model of pandemic
approximate dual dynamic programming
sufficient approximate optimality conditions for Nash equilibrium
numerical algorithm
Opis:
We build a mathematical game model of pandemic transmission, including vaccinations of population and budget costs of different acting to eliminate pandemic. We assume the interactions among different groups: vaccinated, susceptible, exposed, infectious, super-spreaders, hospitalized and fatality, defining a system of ordinary differential equations, which describes compartment model of disease and costs of the treatment. The goal of the game is to describe the development disease under different types of treatment, but including costs of them and social restrictions, during the shortest time period. To this effect we construct a dual dynamic programming method to describe open-loop Nash equilibrium for treatment, a group of people having antibodies and budget costs. Next, we calculate numerically an approximate open-loop Nash equilibrium.
Źródło:
Archives of Control Sciences; 2023, 33, 3; 651--680
1230-2384
Pojawia się w:
Archives of Control Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 29

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