Yes, space-based solar power will be feasible in the near future. It is already possible to put satelites in to space surrounding the Earth, and indeed has been possible since the 1960s. There is no reason to think that space-based solar panels are not possible, then, so it is only a matter of time before it happens.
Solar is the way of the future. It becomes more and more efficient as time goes on and more research into the technology is done. Because of this combined with the increased private exploration into space technologies, space-based solar power would be a natural progression. The fact there could be 24 hour sunlight 365 days a week also makes the idea more appealing.