Optimal Power Consumption Motion Control of a Fish-Like Vehicle in a Vortices Vector Field

This article concerns the formalization of a control framework for the fish-like motion control in a fluid due to a vector field generated by point vortices so that the overall power consumption required to travel between the departure and the arrival points is minimized. The control action is synthesized by specifying the time, location and circulation of at least one vortex and the extent to which this vortex, together one or more other vortices will propel the mobile platform considered as a point particle. Given the complexity of the general problem, we consider two simplifying assumptions: (i) only two vortices are active at each time interval, and (ii) the motion takes place in R-2. Necessary conditions of optimality in the form of a Maximum Principle of Pontryagin are stated, and the features ensuring that they constitute a solid basis for the synthesis of the optimal control strategy are discussed.