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4 Qualifying Exam/2 Writing/2. QE State of the Art.md
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@ -29,9 +29,11 @@ b_{min} \leq b +e_b \leq b_{max} \\
k_{min} \leq k +e_k \leq k_{max}} $$ k_{min} \leq k +e_k \leq k_{max}} $$
where $e_m$ is the difference between the nominal mass and the actual as-built mass. $e_b$ and $e_k$ follow similar logic. Structured perturbations are easy to use to create perturbed plants: simply pick values for $e_m$, $e_b$, and $e_k$ that are within the allowable bounds and plug them in to create a new, perturbed transfer function. where $e_m$ is the difference between the nominal mass and the actual as-built mass. $e_b$ and $e_k$ follow similar logic. Structured perturbations are easy to use to create perturbed plants: simply pick values for $e_m$, $e_b$, and $e_k$ that are within the allowable bounds and plug them in to create a new, perturbed transfer function.
Structured perturbations also require a lot of leg work to create
**Limitation:** *Structured perturbations limit the form of perturbation possible to sample.* Because structured perturbations either are chosen a priori or through a parametric study, the form of possible perturbed plants is limited. Structured perturbations do not allow for unmodelled dynamics to be included as a possible perturbation. **Limitation:** *Structured perturbations limit the form of perturbation possible to sample.* Because structured perturbations either are chosen a priori or through a parametric study, the form of possible perturbed plants is limited. Structured perturbations do not allow for unmodelled dynamics to be included as a possible perturbation.
The other type of uncertainty considered is unstructured uncertainty. This type of uncertainty does not assume a form and thus is able to capture unmodelled behavior in its robustness analysis. Unstructured sets are advantageous compared to structured sets for this reason. Robustness with respect The other type of uncertainty considered is unstructured uncertainty. This type of uncertainty does not assume a form and thus is able to capture unmodelled behavior in its robustness analysis. Unstructured sets are advantageous compared to structured sets for this reason. Robustness with respect to unstructured sets provides a guarantee of resilience to adverse conditions that are unanticipated, or difficult to model.
(The disk multiplicative perturbation) (The disk multiplicative perturbation)