  In this paper, we study a problem of controlling cooling facilities and
computational equipments for energy-efficient operations of data centers.
Although a plethora of approaches have been proposed in previous literatures,
there is a lack of rigorous methodologies for effectively addressing the
problem. To bridge this gap, we propose MPC frameworks for jointly and
optimally tuning the Computer Room Air Conditioner (CRAC) supplying air
temperature as well as the number of active servers for minimizing the overall
energy consumption. We specifically find that, when a standard model of data
centers with contained cold aisles and cooling facilities are used, the
optimization problems arising from the MPC framework can be transformed to
convex optimization problems that can be solved efficiently. We present several
numerical simulations to illustrate the effectiveness of our theoretical
results.
