Given that the inverse trigonometric functions assume principal values only. Let $x,y\in[-1,1]$ such that $\cos^{-1}x-\sin^{-1}y=\alpha$, with $-\dfrac{\pi}{2}\le\alpha\le\pi$. Then, the minimum value of $x^{2}+y^{2}+2xy\sin\alpha$ is: