Temat: second-order necessary conditions - Katalog OPAC zbiorów

Skocz do pozycji: 1.

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

Zmień widok

na półce

Skocz do pozycji: 2.

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

Zmień widok

na półce

Skocz do pozycji: 3.

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

Zmień widok

na półce

Skocz do pozycji: 4.

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

Zmień widok

na półce

Informacja

Wyszukujesz frazę "second-order necessary conditions" wg kryterium: Temat

Źródło danych

Dostawca treści

Kolekcja

Rok wydania

Wydawca

Temat

Autor

Typ dokumentu

Język