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. 
@article{TM_2010_268_a4,
     author = {R. W. Brockett},
     title = {On the control of a~flock by a~leader},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {56--63},
     publisher = {mathdoc},
     volume = {268},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2010_268_a4/}
}
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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/