Low-Cost Dynamic Voltage and Frequency Management Based upon Robust Control Techniques under Thermal Constraints

Nonlinear and asymmetric thermal-aware DVFS control

“…In the symmetric case (i.e. ε ≈ 1), the simple relations observed in [14] are confirmed here but the non-linearity highly complexifies the relations. Thus, whereas the average temperature only increases w.r.t.…”

“…On the other hand, hot spots can be reduced thanks to the chopped scheme. We already showed in [14] that the steady-state average temperature and its ripple depend on both parameters and the maximal attained temperature highly depends on the switching control. Even if the relation with these parameters is more complex in the nonlinear case, such an observation can be done (simulation results are not provided due to space limitation).…”

“…in number of instructions per second) and adapts the control variables with respect to a computational load to treat (in terms of number of instructions and deadline for each task to execute). One can refer to [6], [14] for further details.…”

“…In practice, it could be constant or fixed by a given criterion to satisfy. Such a method is treated in [14] in particular, where the product κτ is fixed, and so is the energy-temperature tradeoff. The suggested idea is based on the fact that i) a small period leads to small variations and ii) fast oscillations increase the energy consumption (because the transitions consume some power that is not strictly speaking used for the computations).…”

“…with ξ 1 (n) := ς(n)e (β1−β2)κτ ξ 2 (n) := ς(n) ς(n) := e −n((β1−β2)κ+β2)τ and σ 1 := +1 σ 2 := −1 Note that the term ξ i (•) exhibits an exponential decrease. Moreover, the initial temperature slope µ(n = 0) can be expressed from (11) and (14). Then, at each new oscillating period, the slope is equal to the previous one plus an extra term η defined as follows…”