Publicação
A control problem with passive particles driven by point vortices on the sphere
| Resumo: | The objective of this study is to control the motion of a passive particle advected by N point vortices in a sphere. The square of the L2 norm of control, necessary for the system to evolve from a starting point to an end point in an a priori fixed time, must be minimized. If the motion is generated by a single vortex (N=1), we show that the system is controllable. The problem is also solved by a direct approach, where the control problem is transformed into a nonlinear optimization problem that is solved numerically. In the case of one (N=1), two (N=2), or three (N=3) point vortices, the numerical results show the existence of near/quasi-optimal control. |
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| Autores principais: | Balsa, Carlos |
| Outros Autores: | Gama, Sílvio M.A. |
| Assunto: | Vortex motion Passive tracer Spherical motion Optimal control Non-linear optimization problem |
| Ano: | 2022 |
| País: | Portugal |
| Tipo de documento: | comunicação em conferência |
| Tipo de acesso: | acesso restrito |
| Instituição associada: | Instituto Politécnico de Bragança |
| Idioma: | inglês |
| Origem: | Biblioteca Digital do IPB |
| Resumo: | The objective of this study is to control the motion of a passive particle advected by N point vortices in a sphere. The square of the L2 norm of control, necessary for the system to evolve from a starting point to an end point in an a priori fixed time, must be minimized. If the motion is generated by a single vortex (N=1), we show that the system is controllable. The problem is also solved by a direct approach, where the control problem is transformed into a nonlinear optimization problem that is solved numerically. In the case of one (N=1), two (N=2), or three (N=3) point vortices, the numerical results show the existence of near/quasi-optimal control. |
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