High contrast imaging from space relies on coronagraphs to limit diffraction and a wavefront control systems to compensate for imperfections in both the telescope optics and the coronagraph. The extreme contrast required (up to 10^-10 for terrestrial planets) puts severe requirements on the wavefront control system, as the achievable contrast is limited by the quality of the wavefront. This paper presents a general closed loop correction algorithm for high contrast imaging coronagraphs by minimizing the energy in a predefined region in the image where terrestrial planets could be found. The estimation part of the algorithm reconstructs the complex field in the image plane using phase diversity caused by the deformable mirror. This method has been shown to achieve faster and better correction than classical speckle nulling.