Network optimality conditions

• Autorzy: Osmolovskii Nikolai P. , Qian Meizhi , Sokołowski Jan

Identyfikatory

DOI

10.2478/candc-2023-0035

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

network; optimal control problem; weak local minimum; Pontryagin’s maximum principle; critical cone; quadratic form; second order optimality conditions; Riccati equation

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2023
• Tom: Vol. 52, No. 2
• Strony: 129--180
• Opis fizyczny: Bibliogr. 15 poz., rys.

Twórcy

autor

Osmolovskii Nikolai P.

• Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447 Warszawa, Poland

autor

Qian Meizhi

• Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447 Warszawa, Poland
• School of Mathematical Sciences, East China Normal University, Shanghai 200241, China

autor

Sokołowski Jan

• Systems Research Institute, Polish Academy of Sciences, ul. Newelska 6, 01-447 Warszawa, Poland
• Institut Élie Cartan de Lorraine, UMR 7502, Université de Lorraine, B.P. 70239, 54506 Vandoeuvre-lés-Nancy Cedex, France

Bibliografia

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