A two-layer distributed MPC approach to thermal control of Multiprocessor Systems-on-Chip

Next-generation Multiprocessor, or Multicore, Systems-on-Chip offer very high computing performance at the expense of a very high power density unevenly distributed on the chip. The hot spots thus generated represent a significant source of performance and reliability degradation, as well as power consumption increase. In recent years, run-time thermal control strategies have been developed to deal with this issue by acting on some "computational knobs" (e.g., clock frequencies and supply voltages). In this context, schemes based on Model Predictive Control (MPC) are particularly suitable due to their capability to deal with constraints explicitly. In this paper, we first discuss relevant properties for the design of predictive controllers for thermal systems. Starting from the Partial Differential Equation (PDE) describing heat diffusion in a solid, we prove meaningful feasibility properties that can be leveraged for constraint reduction. We then present a procedure to derive approximated but effective modular thermal models intended to build an efficient distributed MPC. Finally, a two-layer control solution is proposed to maximize performance while preserving feasibility despite model approximations. The effectiveness of this approach is validated through extensive and realistic numerical simulations.