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    Wyświetlanie 1-6 z 6
    Tytuł:
    Second-order sufficient conditions for an extremum in optimal control
    Autorzy:
    Osmolovskij, N.
    Powiązania:
    https://bibliotekanauki.pl/articles/206727.pdf
    Data publikacji:
    2002
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    ekstremala łamana
    forma kwadratowa
    minimum silne
    minimum słabe
    stożek krytyczny
    warunek dostatecznej optymalności
    zasada maksimum
    accessory problem
    broken extremal
    control discontinuities
    critical cone
    maximum principle
    quadratic form
    strong minimum
    suffcient optimality condition
    weak minimum
    Opis:
    Suffcient quadratic optimality conditions for a weak and a strong minimum are stated in an optimal control problem on a fixed time interval with mixed state-control constraints, under the assumption that the gradients of all active mixed constraints with respect to control are linearly independent. The conditions are stated for the cases of both continuous and discontinuous controls and guarantee in each case a lower bound of the cost function increase at t1e reference point. They are formulated in terms of an accessory problem with quadratic form, which must be positive-definite on the so-called critical cone. In the case of discontinuous control the quadratic form has some new terms related to the control discontinuity.
    Źródło:
    Control and Cybernetics; 2002, 31, 3; 803-831
    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:
    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:
    Network optimality conditions
    Autorzy:
    Osmolovskii, Nikolai P.
    Qian, Meizhi
    Sokołowski, Jan
    Powiązania:
    https://bibliotekanauki.pl/articles/31343935.pdf
    Data publikacji:
    2023
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    network
    optimal control problem
    weak local minimum
    Pontryagin’s maximum principle
    critical cone
    quadratic form
    second order optimality conditions
    Riccati equation
    Opis:
    Optimality conditions for optimal control problems arising in network modeling are discussed. We confine ourselves to the steady state network models. Therefore, we consider only control systems described by ordinary differential equations. First, we derive optimality conditions for the nonlinear problem for a single beam. These conditions are formulated in terms of the local Pontryagin maximum principle and the matrix Riccati equation. Then, the optimality conditions for the control problem for networks posed on an arbitrary planar graph are discussed. This problem has a set of independent variables xi varying within their intervals [0, li], associated with the corresponding beams at network edges. The lengths li of intervals are not specified and must be determined. So, the optimization problem is non-standard, it is a combination of control and design of networks. However, using a linear change of the independent variables, it can be reduced to a standard one, and we show this. Two simple numerical examples for the single-beam problem are considered.
    Źródło:
    Control and Cybernetics; 2023, 52, 2; 129-180
    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:
    A second-order sufficient condition for a weak local minimum in an optimal control problem with an inequality control constraint
    Autorzy:
    Osmolovskii, Nikolai P.
    Powiązania:
    https://bibliotekanauki.pl/articles/2183496.pdf
    Data publikacji:
    2022
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    critical cone
    quadratic form
    first order tangent
    second order tangent
    second order optimality conditions
    weak local minimum
    inequality control constraint
    Pontryagin’s maximum principle
    Opis:
    This paper is devoted to a sufficient second-order condition for a weak local minimum in a simple optimal control problem with one control constraint G(u) ≤ 0, given by a C2-function. A similar second-order condition was obtained earlier by the author for a strong minimum in a much more general problem. In the present paper, we would like to take a narrower perspective than before and thus provide shorter and simpler proofs. In addition, the paper uses the first and second order tangents to the set U, defined by the inequality G(u) ≤ 0. The main difficulty of the proof, clearly shown in the paper, refers to the set, where the gradient Hu of the Hamiltonian is small, but the condition of quadratic growth of the Hamiltonian is satisfied. The paper can be valuable for self-explanation and provides a basis for extensions.
    Źródło:
    Control and Cybernetics; 2022, 51, 2; 151--169
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-6 z 6

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