How did building the Palace of Versailles give King Louis XIV control over the French nobility?

Answer:

King Louis XIV, who reigned longer than any other King in history, had big ideas. One of them was that the whole of the nobility ought to live with him in his palace, where he could keep an eye on them. As the Louvre was too small, he began a new palace at Versailles, ten miles out of Paris to the South-West. 2000 rooms, and a garden with a pond a mile long. Room for everybody, if a bit cramped. If you were a Duke you might get three rooms to live in and the supreme honour of holding the King's shirt when he got dressed. Everything the King did, he did in public. Often twice, to fit in all the spectators.

Surprisingly, it worked. The civil wars which had marred the first half of his reign stopped dead; all the people who might have started them were busy holding shirts and observing rigid etiquette. He also started various foreign wars to absorb their appetite for bloodshed.

Of course, the building and the wars between them bankrupted the country, but hey, that was a problem for his cuccessors.