This paper presents a two-time-scale control method to optimize the energy consumption of high-performance-computing data centers through dynamic frequency scaling of processors, tasks assignment, and cooling supplement. First, the steady and dynamical models of the data center are built, which reflect the computational interactions and thermal relationship among the components of the data center. Next, the energy minimization problem for processing a parallel task is divided into two parts that correspond to the steady thermal model and the dynamic thermal one. Then, the problem is solved in a two-time-scale manner, i.e., the optimization of task assignment and processing frequency is considered in steady thermal environment, and the optimization of cooling supplement is achieved in dynamic thermal environment. Finally, simulations of a real task trace are carried out, which demonstrate that the proposed method can significantly improve energy efficiency while guaranteeing the thermal constraints of the data center.

The aim of this note is to study the quantum robust optimal control problem for a class of linear quantum systems with uncertainties. It is shown that such problem can be converted into a mixed linear quadratic Gaussian and $H^{\infty }$ quantum control problem. A physical model described by complex quantum stochastic differential equations (CQSDEs) is presented for the quantum system with uncertainties. The quantum system described by CQSDEs is called a complex quantum system in terms of annihilation and creation operators (Maalouf and Petersen, 2011). For an uncertain quantum system, we build a connection with a scaled linear system without uncertainty. The desired quantum robust optimal control results are derived based on the connection. We provide one numerical procedure for quantum robust optimal controller synthesis and then provide an example. The resulting controller presents robustness and optimal performance.