Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

The first constraint, Equation 5.6, requires the tailoring for tuning dummy variable,
z1, to be greater than or equal to the maximum tuned performance over the uncer-
tainty vertices. Equation 5.7 is equivalent to Equation 3.6 from the AO formulation,
and requires that z2 be greater than or equal to the maximum un-tuned performance
over the uncertainty space. Since the objective is to minimize a weighted sum of z1
and z2, the constraints ensure that these variables are effectively the worst-case tuned
and worst-case untuned performances, respectively.
In this form, the analytical gradients of the cost function are easily derived by
inspection:
∂JRP T T
∂�x = �0
∂JRP T T
∂�yi
= �0
∂JRP T T
∂z1
=1− α
∂JRP T T
∂z2
= α (5.8)
Constraint gradients are also required for a constrained gradient-based optimization.
The gradients of the parameter constraints, �g, depend on the particular design prob-
lem under consideration. The augmented constraint gradients include the gradients
of the performance with respect to the tailoring and tuning parameters:
∂h1i
∂�x
∂h2i
∂�x
∂f (�x, �yi,�pi)
=
∂�x
∂f (�x, �y0,�pi)
=
∂�x
∂h1i
∂�yi
∂h2i
∂�yi
= ∂f (�x, �yi,�pi)
∂�yi
= �0
∂h1i
∂z1
∂h2i
∂z1
= −1
=0
∂h1i
∂z2
∂h2i
∂z2
=0 (5.9)
= −1 (5.10)
In the following section the RPTT optimization is applied to the design of a
structurally connected interferometer using the SCI development model. A variety
of optimization algorithms are used to solve the problem and the performance of the
different formulations are compared for efficiency.
5.2 SCI Development Model
Application of the RPTT methodology to the SCI development model requires all of
the elements presented in the previous chapters. The tailoring parameters are the
two cross-sectional areas (Table 2.3), the tuning parameters are the design masses
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