Balsa, CarlosGama, Sílvio M.A.2023-05-102023-05-102020Balsa, Carlos; Gama, Sílvio (2020). The numerical control of the motion of a passive particle in a point vortex flow. In 14th International Conference on Automatic Control and Soft-Computing CONTROLO’2020. Bragançahttp://hdl.handle.net/10198/28261This work reports numerical explorations in the advection of one passive tracer by point vortices living in the unbounded plane. The main objective is to find the energy-optimal displacement of one passive particle (point vortex with zero circulation) surrounded by N point vortices. The direct formulation of the corresponding control problems is presented for the case of N = 1, N = 2, N = 3 and N = 4 vortices. The restrictions are due to (i) the ordinary differential equations that govern the displacement of the passive particle around the point vortices, (ii) the available time T to go from the initial position z0 to the final destination zf; and (iii) the maximum absolute value umax that is imposed on the control variables. The resulting optimization problems are solved numerically. The numerical results show the existence of nearly/quasi-optimal control.engconference object