  Groups of aircraft have the potential to save significant amounts of energy
by flying in formations; all but the leading aircraft can benefit from the
upwash of the wakes of preceding aircraft. A potential obstacle as the number
of aircraft in such a formation increases is that disturbances at one aircraft,
for example caused by turbulence or wake meandering, can propagate and grow as
each following aircraft tries to track the optimal energy-saving position
relative to the one in front. This phenomenon, known as string instability, has
not yet been adequately examined in the context of aircraft formations. We
discuss some trade-offs involved in designing string stable controllers whose
objective is to minimize energy, and present a control design method to achieve
both string stability and energy efficiency of an aircraft formation. In
simulations of a 10-aircraft linear formation in the presence of 2% turbulence
intensity, our controller achieves string stability while reduced energy
consumption by an average of 13% with respect to solo flight.
