The ever growing demand of more resolution for ground telescopes makes of fundamental importance the use of computationally efficient algorithms. In this paper we consider some efficient algorithms for the adaptive optics system of large telescopes. The main peculiarities of the considered procedures are to be effective and scalable to telescopes of whatever size. In particular, we propose a decoupled representation of the turbulent phase in which each of the subsystems models the temporal dynamic of a turbulent mode (e.g. the evolution of a Zernike mode if using the Zernike bases to represent the turbulence). The model matrices are identified using recently developed subspace methods. Then, using it in a Kalman-based approach, it provides good performances for the closed-loop system. Furthermore, we analyze and compare other possible approaches, such as PI controllers and AR predictive models. Since computational efficiency plays a very important role in this framework, we evaluate the obtained results both for the absolute performances and for the computational efforts necessary to obtain them. The proposed Kalman-based model ensures a good tradeoff between complexity and performances. Anyway, when the system allows to use some more resources, it can be worth to consider the use of high order AR models.