Optimal Multi-process Control of a Two Vortex Driven Particle in the Plane

This article concerns the optimal motion control of a particle moving in a two dimensional fluid whose dynamics are given by a vector field defined, in any time interval, by two point vortices whose circulation decay exponentially in time with a given constant rate. The control action is exercised by generating one vortex - specified by its location and respective circulation - at a chosen time, and by varying the exposure of the particle to each one of the vortices in continuum time. A control multi-process framework is chosen in order to derive necessary conditions of optimality in the form of a Maximum Principle of Pontryagin. These conditions provide relations that suffice to fully determine the optimal control process. © 2017