Geodesic
On the Computation of Hierarchical Control results for One-Dimensional Transmission Line
Mathematica Applicanda, Tome 50 (2022) no. 1, pp. 107-128.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

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.
DOI : 10.14708/ma.v50i1.7151
Mots-clés : Controllability, Stackelberg strategy, Transmission line equation, Numerical Simulation. 
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Pitagoras Pinheiro de Carvalho; Isaias Pereira de Jesus; Olimpio Pereira de Sá Neto. On the Computation of Hierarchical Control results for One-Dimensional Transmission Line. Mathematica Applicanda, Tome 50 (2022) no. 1, pp.  107-128. doi : 10.14708/ma.v50i1.7151. http://geodesic.mathdoc.fr/articles/10.14708/ma.v50i1.7151/

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