Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

is considered.
4.2.1 Hardware-only Tuning
One approach to the problem is to perform a tuning optimization and replace per-
formance predictions from the model with hardware data. In effect, a real-time
optimization is conducted using the hardware and test data. At each iteration of
a gradient-based optimization algorithm the cost function, f (xk), is evaluated, the
gradient of the objective is calculated and a new search direction and step-size are ob-
tained. The use of a model in this process allows for quick computation and analytical
gradient calculations.
Replacing the model simulation with actual test data is both computationally
expensive and labor intensive as each function call requires an actual hardware test.
In addition, analytical gradients are no longer available and finite-difference approx-
imations must be used instead. There are two methods to compute finite-difference
gradients, the forward-difference and central-difference equations:
∂f (x)
∂xi
∂f (x)
∂xi
= f (x +∆xei) − f (x)
∆x
= f (x +∆xei) − f (x − ∆xei)
2∆x
(4.3)
(4.4)
where i denotes an element of x, ei is a unit vector with a 1 in the i th location,
and ∆x is a small change in the design parameter. The central difference equation
(Equation 4.4) is more accurate, but requires an additional function evaluation at
each step. These approximations are both sensitive to the size of ∆x, and large
parameter changes may be outside the range of linear approximation. The need to
use finite-difference gradient approximations adds to the time and cost burden of
real-time tuning optimizations.
A second consideration of hardware optimizations is that it is not always possible
to evaluate iterates that are beyond the constraint boundaries. In the example of mass
tuning considered in this chapter there are two constraints: a total mass constraint
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