Optimal route planning in steady planar convective flows

Abstract

We consider the following optimal control problem with state constraints: find optimal route between two given points in a planar steady convective flow. The cost function is a weighted sum of the total traveling time and the energy spent by the controller. The optimal control problem is solved numerically by using an indirect method based on Pontryagin’s Maximum Principle in the Gamkrelidze’s form. Optimal routes are computed and discussed for three examples of convective flows.