Dynamic coverage optimal control of interferometric imaging spacecraft formations

In this paper, we study dynamic coverage optimal control, which is a new class of optimal control problems motivated by multi-spacecraft interferometric imaging applications. The dynamics is composed of N second order differential equations representing N fully actuated particles. To be minimized is a cost functional that is a weighted sum of the total fuel expenditure, the relative speeds between the particles and the measure of a given set whose size is a function of the particles´ trajectories. We derive optimality conditions and give a simple three spacecraft example to illustrate the concepts and ideas presented in the paper.