Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-08T05:33:01.315Z Has data issue: false hasContentIssue false

7 - Static Systems: Set-Theoretic Input Uncertainty

Published online by Cambridge University Press:  17 January 2022

Alejandro D. Domínguez-García
Affiliation:
University of Illinois, Urbana-Champaign
Get access

Summary

This chapter covers the analysis of static systems under set-theoretic input uncertainty. In the first part of the chapter, we assume that the input belongs to an ellipsoid and analyze both linear and nonlinear systems. For the linear case, we provide techniques to exactly characterize the set containing all possible values that the state can take. For the nonlinear case, we again resort to linearization to approximately characterize the set containing all possible values that the state can take. The second part of the chapter considers linear and nonlinear systems when the input is known to belong to a zonotope. For the linear case, we are able to compute the exact set containing all possible values the state can take, whereas for the nonlinear case, we settle for an approximation thereof obtained via linearization. The techniques developed are utilized to analyze the power flow problem under uncertain active power injections.

Type
Chapter
Information
Large-Scale System Analysis Under Uncertainty
With Electric Power Applications
, pp. 202 - 236
Publisher: Cambridge University Press
Print publication year: 2022

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×