Middleton, Richard H. and Braslavsky, Julio H.
String Instability in Classes of Linear Time Invariant
Formation Control With Limited
IEEE Transactions on Automatic Control, 55 (7).
This paper gives sufficient conditions for string instability
in an array of linear time-invariant autonomous vehicles
with communication constraints. The vehicles are controlled
autonomously and are subject to a rigid or semi-rigid formation
policy. The individual controllers are assumed to have a limited
range of forward and backward communication with other vehicles.
Sufficient conditions are given that imply a lower bound
on the peak of the frequency response magnitude of the transfer
function mapping a disturbance to the leading vehicle to a vehicle
in the chain. This lower bound quantifies the effect of spacing
separation policy, intervehicle communication policy, and vehicle
settling response performance. These results extend earlier works
to give a unified treatment of heterogeneous, non-nearest neighbor
communication and semi-rigid one-dimensional formation control.
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