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.