vault backup: 2024-08-29 15:53:58

This commit is contained in:
Dane Sabo 2024-08-29 15:53:58 -04:00
parent b0f11b3dbd
commit d30bd9c3ca
4 changed files with 108 additions and 17 deletions

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## For reading papers:
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# Take 1
<mark style="background: #ABF7F7A6;">Controllers in the real world control plants that are not perfectly represented by a mathematical model. For this reason, controllers that operate in high-assurance environments must be evaluated to be robust.</mark>
<mark style="background: #ABF7F7A6;"><mark style="background: #FFF3A3A6;">Controllers</mark> in the real world <mark style="background: #FFF3A3A6;">control</mark> plants that are not perfectly represented by a mathematical model. For this reason, <mark style="background: #FF5582A6;">controllers</mark> that operate in high-assurance environments must be evaluated to be robust.</mark>
<mark style="background: #FFB8EBA6;">Validation and verification of controller robustness is done today, but is a strenuous, manual task.</mark>
Examining the robustness of a <mark style="background: #FFF3A3A6;">controller</mark> requires additional mathematical formalism of a system, and analysis of perturbations to a nominal plant model.
Perturbations can be considered as two forms--structured and unstructured perturbation.
Unstructured perturbation in particular allows the perturbation to take on any transfer function (or transfer matrix), such that the gain of the transfer function remains less than one.
<mark style="background: #FFB86CA6;">Examining the robustness of a <mark style="background: #FFF3A3A6;">controller</mark> requires additional mathematical formalism of a system, and analysis of perturbations to a nominal plant model.</mark>
<mark style="background: #FF5582A6;">Perturbations can be considered as two forms--structured and unstructured perturbation.</mark>
<mark style="background: #ADCCFFA6;">Unstructured perturbation in particular allows the perturbation to take on any transfer function (or transfer matrix), such that the gain of the transfer function remains less than one.</mark>
If a controlled system remains stable for the nominal plant and all possible perturbations, it is considered robust.
To actually validate this statement with actual perturbations is a difficult problem.
Generating perturbations is not trivial because there is so much possibility for the form of an unstructured perturbation.