Geodesic
On the control of a~flock by a~leader
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and topology. I, Tome 268 (2010), pp. 56-63.

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The collective and individual behaviors of the elements of a set of identical units are investigated from the point of view of their response to a coordination signal broadcast by a leader. In terms of the model used here, we show that for such systems nonlinearity plays a critical role. A new method for establishing controllability of nonlinear, replicated systems is given. Similarly, stabilization also depends on high order nonlinear effects. For the purpose of stabilization, a distinction between odd order nonlinear terms and even order nonlinear terms plays a role. 
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     author = {R. W. Brockett},
     title = {On the control of a~flock by a~leader},
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R. W. Brockett. On the control of a~flock by a~leader. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and topology. I, Tome 268 (2010), pp. 56-63. http://geodesic.mathdoc.fr/item/TM_2010_268_a4/

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