Freshwater-saltwater boundary detection using mobile sensors part II: Drifter movement

In this paper, we study the minimum energy control problem in a flow environment, in which the flow is described by a quadratic function and the objective is to minimize the energy consumption while driving drifters from one point to another. The minimum energy control problem is motivated by the fact that mobile drifters are powered by batteries of limited capacity. We first derive the unconstrained optimal control using the Pontryagin's minimum principle, and then take into account state constraints that arise naturally in our setting. If the dynamics of drifters are restricted to be of Dubin's type, the optimal control is in the form of state feedback, which potentially leads to more robust implementation.