Temat: Pontryagin minimum - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: On the development of Pontryagins Maximum Principle in the works of A.Ya. Dubovitskii and A.A. Milyutin
Autorzy:: Dmitruk, A. V.
Tematy:: Euler-Lagrange equation
maximum principle
classes of variations
Pontryagin minimum
state constraints
measure in adjoint equation
regular and nonregular mixed constraints
phase points
closure with respect to measure
three-storey theorem; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Powiązania:: https://bibliotekanauki.pl/articles/970915.pdf Link otwiera się w nowym oknie
Opis:: We give a short review of the development and generalizations of the Pontryagin Maximum Principle, provided in the studies of Dubovitskii and Milyutin in the 1960s and later years.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Network optimality conditions
Autorzy:: Osmolovskii, Nikolai P.
Qian, Meizhi
Sokołowski, Jan
Tematy:: network
optimal control problem
weak local minimum
Pontryagin’s maximum principle
critical cone
quadratic form
second order optimality conditions
Riccati equation; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Powiązania:: https://bibliotekanauki.pl/articles/31343935.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

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.
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; Pokaż więcej
Wydawca:: Polska Akademia Nauk. Instytut Badań Systemowych PAN
Powiązania:: https://bibliotekanauki.pl/articles/2183496.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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