An Iterative Algorithm to Estimate Invariant Sets for Uncertain Systems

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

This paper develops an iterative algorithm to estimate an invariant set for uncertain systems. The uncertain system is given as a connection of a nominal linear time-invariant system and a perturbation. The input/output behavior of the perturbation is described by integral quadratic constraints (IQCs). The proposed approach incorporates IQCs into a dissipation inequality formulation. One issue is that it is often useful to specify the IQC in the frequency domain or, equivalently, in the time-domain as a 'soft' infinite-horizon constraint. However, the dissipation inequality formulation requires constraints that are valid over all finite time horizons. The main technical result is a finite-horizon bound on soft IQCs constructed using a state-feedback transformation. This forms the basis for the proposed iterative algorithm to estimate invariant sets. A simple example is provided to demonstrate the proposed approach.

Original languageEnglish (US)
Title of host publication2018 Annual American Control Conference, ACC 2018
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4249-4254
Number of pages6
ISBN (Print)9781538654286
DOIs
StatePublished - Aug 9 2018
Event2018 Annual American Control Conference, ACC 2018 - Milwauke, United States
Duration: Jun 27 2018Jun 29 2018

Publication series

NameProceedings of the American Control Conference
Volume2018-June
ISSN (Print)0743-1619

Other

Other2018 Annual American Control Conference, ACC 2018
Country/TerritoryUnited States
CityMilwauke
Period6/27/186/29/18

Bibliographical note

Funding Information:
The work was supported by the National Science Foundation under Grant No. NSF-CMMI-1254129 entitled “CAREER: Probabilistic Tools for High Reliability Monitoring and Control of Wind Farms.” Peter Seiler is with the Aerospace Engineering and Mechanics Department, University of Minnesota, Email: seile017@umn.edu.

Publisher Copyright:
© 2018 AACC.

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