This paper considers the Rosenau equation with a moving control
$${partial _t}u + {partial _t}partial _x^4u + {partial _x}u + u{partial _x}u = a(x + ct)h(x,t),c ne 0,x in T = mathbb{R}/(2pi mathbb{Z}),t > 0$$
. The authors prove that the Rosenau equation with a moving control is locally exact controllable in
H s (T) with
s ≥ 0 and globally exponential stable in
H s (T) with
s ≥ 2. The two results nontrivially extend the work of (Rosier L and Zhang B Y, 2013) from the BBM equation to the Rosenau equation.