- 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