Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

where the notation yij indicates the j th tuning parameter at the i th uncertainty vertex.
Keep in mind, that the �yi vectors are only the tuning configuration at the vertices of
the uncertainty space and are not necessarily the final values of the tuning paramters.
The hardware tuning process discussed in Chapter 4 must still be employed if the
hardware realization does not meet requirements. However, the assumption is that if
�x is chosen during tailoring such that the system is tunable at the uncertainty vertices
then the actual hardware will be tunable across the entire uncertainty space. In this
formulation, JTT and JRP T T are almost identical except that the tuning parameters
are allowed to change with the uncertainty vertices in JTT.
The formulation in Equation 5.3 improves the computational efficiency of the
tailoring optimization since tuning optimizations are no longer required at each eval-
uation of the objective function. However the optimization is still a combination of
min-max formulations, and it is unclear how to obtain the analytical gradients. It is
possible to further simplify the RPTT formulation by posing it as a simple minimiza-
tion problem similar to the minimization form of anti-optimization (Equation 3.5):
min
�x,�yi,�z
�
JTT
����
(1 − α) z1 +α
s.t �g (�x, �yi) ≤ �0
JRP T
����
z2
h1i (z1,�x, �yi,�pi) ≤ 0
h2i (z2,�x, �pi) ≤ 0
∀i =1...npv
�
(5.5)
In this formulation the cost function consists only of the weighted sum of two dummy
variables, z1 and z2. The tailoring for tuning and robustness metrics are included
through the augmented constraints:
h1i (z1,�x, �yi,�pi) = −z1 + f (�x, �yi,�pi) (5.6)
h2i (z2,�x, �pi) = −z2 + f (�x, �y0,�pi) (5.7)
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