On the computation of hierarchical control results for one-dimensional transmission line

• Autorzy: Pinheiro de Carvalho Pitagoras , Pereira de Jesus Isaías , Pereira de Sá Neto Olimpio

Identyfikatory

DOI

10.14708/ma.v50i1.7151

Warianty tytułu

PL

O obliczeniowych zadaniach przy wyznaczaniu sterowań hierarchicznych dla jednowymiarowej linii przesyłowej

• Języki publikacji: EN

Abstrakty

EN

In this paper, motivated by a physics problem, we investigate some numerical and computational aspects for the problem of hierarchical controllability in one-dimensional wave equation in domains with a moving boundary. Some controls act in part of the boundary and define a strategy of equilibrium between them, considering a leader control and a follower. Thus, we introduced the concept of hierarchical control to solve the problem and mapped the Stackelberg Strategy between these controls. The numerical methods described here consist of a combination of the following: finite element method (FEM) for space approximation; finite difference method (FDM) for time discretization and fixed-point algorithm for the solution of the total discrete control problem. Data programming and computer simulations are performed in FreeFem++ and for a better presentation of the experiments we use Matlab.

PL

W tym artykule, motywowanym problemem fizycznym, badamy pewne aspekty numeryczne i obliczeniowe problemu sterowalności hierarchicznej w jednowymiarowym równaniu falowym w domenach z ruchomą granicą. Niektóre sterowania są na brzegu i definiują strategię równowagi między nimi, biorąc pod uwagę sterowania lidera i naśladowcę. W związku z tym wprowadziliśmy koncepcję sterowań hierarchicznych w celu rozwiązania tego problemu i przyporządkowaliśmy strategię Stackelberga między tymi strategiami. Opisane tutaj metody numeryczne składają się z kombinacji następujących elementów: metoda elementów skończonych (MES) dla aproksymacji przestrzennej; metoda różnic skończonych (FDM) do dyskretyzacji czasu i algorytm stałoprzecinkowy do rozwiązania problemu całkowitego sterowania dyskretnego. Programowanie danych i symulacje komputerowe wykonujemy w FreeFem++, a dla lepszej prezentacji eksperymentów używamy Matlaba.

Słowa kluczowe

EN

controllability; Stackelberg strategy; transmission line equation; numerical simulation

PL

sterowalność; strategia Stackelberga; linia długa; równania telegrafistów; symulacja numeryczna

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Mathematica Applicanda
• Rocznik: 2022
• Tom: Vol. 50, no. 1
• Strony: 107--128
• Opis fizyczny: Bibliogr. 33 poz., rys., tab., wykr.

Twórcy

autor

Pinheiro de Carvalho Pitagoras

• Fundação Universidade Estadual do Piauí: Teresina, Piauí, Brazil

• https://orcid.org/0000-0003-0949-2921

autor

Pereira de Jesus Isaías

• Fundação Universidade Estadual do Piauí: Teresina, Piauí, Brazil

• https://orcid.org/0000-0003-0949-2921

autor

Pereira de Sá Neto Olimpio

• Universidade Estadual do Piauí(UESPI) Coordenação de Ciências da Computação, Parnaíba, PI, Brazil

• https://orcid.org/0000-0003-0215-249X

Bibliografia

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Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).