Putting astroturf over the top of a splintering or warping deck board is like sweeping the dirt under the throw rugs.
You will still feel the warped boards, and the splinters will cause the carpet or vinyl to wear unevenly.
You say the deck is 15 years old, I'd say you got your money's worth. Replace the decking.
My favorite way to demo old decking is to take a circular saw and cross cut the decking on the edge of a couple of joist bays, then take a hammer and pound the boards into the bays so they pry themselves off of the joists. That's the easy but somewhat destructive method. A cleaner and less destructive to the joist method is to cut on each side of the joist bay, then pry the little wood block off with a crowbar.
Or, you could hire a contractor to do it through ImproveNet.com (www.improvenet.com),...