Feasibility of Yuri Milner's Breakthrough Starshot

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TL;DR
How far can laser control of a small spacecraft extend?
I've been reading about Yuri Milner's 'Breakthrough Starshot'. It posits sending a very small craft, less than 1 gram, to Alpha Centauri, by way of a lightsail propelled by an array of lasers fired from Earth. It is proposed that this craft will be able to reach 30% of light speed, i.e. around 100 million kph, and would reach its destination in about 20 years at that speed. Once there, it would send back data on the planets orbiting that star, by signals that would take four years to reach Earth (that system being four light-years distant.)

I'm very interested in this idea and have spent some time perusing their website, but there's one obvious question that strikes me, which is, how far could control be extended by way of a laser beam fired from earth? Surely not the hundreds of billions, or trillions, of kilometers that would seem to be required by this proposal? It seems an obvious defeater for the idea but maybe there's something I don't understand about it.
 
on Phys.org
The lasers are only used during the brief acceleration phase. Of the order of 10 minutes, up to a distance of maybe 2 light minutes or ~30 million km. Afterwards the spacecraft continue on whatever trajectory they got from this acceleration phase. Many will miss, but some can get close enough to be useful.
 
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Right! Well, that's something I missed from watching the intro video and the other materials. Thanks. (I notice that all the news items on the site are from 2016-17 so I wonder if there's been much progress on it.)
 
Quotidian said:
Right! Well, that's something I missed from watching the intro video and the other materials. Thanks. (I notice that all the news items on the site are from 2016-17 so I wonder if there's been much progress on it.)

Large parts of the project have potential military applications. Any progress will be classified.
 
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