Chapter 5 Robust Performance Tailoring with Tuning - SSL - MIT

MPC optimization by allowing a different control sequence for each realization of the
disturbance.
The RPTT cost function is a weighted sum of a tailoring for tuning objective,
JTT, and a robust performance tailoring objective, JRP T :
JRP T T =(1− α)JTT + αJRP T
(5.1)
The weighting parameter, α, allows adjustment of the relative weight between tuning
authority and robustness. If α = 0, the design is tailored for maximum tuning
authority, and if α =1,JRP T T reduces to an RPT optimization. Optimizing for
only JTT could lead to a design that is tunable, but is highly sensitive to uncertainty
and therefore relies heavily on hardware tuning for mission success. Since hardware
tuning requires additional time and resources, the ideal structure is one that will most
likely meet performance, but can be tuned to meet requirements in the event that
the hardware realization falls short. Therefore, it is preferable to find a design that
is both robust to uncertainty and tunable, so that the uncertainty compensation is
shared between robust design and hardware tuning.
One way to formulate the two objectives is with nested optimizations:
min
�x
⎧
⎪⎨
(1 − α)
⎪⎩
�p∈P min
�
�
JRP T
��
⎫
�
⎪⎬
f (�x, �y, �p)
�y∈Y
+α max f (�x, �y0,�p)
�p∈P ⎪⎭
JTT
� �� �
�
max
s.t. g (�x) ≤ �0
(5.2)
The tailoring for tuning cost is a max-min optimization in which the tuning optimiza-
tion, Equation 4.2, is performed at each of the uncertainty vertices. In effect, JTT,is
the worst-case tuned performance over the uncertainty space. The anti-optimization
cost, Equation 3.4, is used as the robust performance tailoring objective. Note that
the difference between JTT and JRP T is that, in the robust objective the tuning pa-
rameters are fixed at their nominal value, �y0 and no tuning optimization is performed.
The outer tailoring optimization is performed only over the tailoring parameters, �x,
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