Robust Analysis of Uncertain ODE-PDE Systems Using PI Multipliers, PIEs and LPIs

Amritam Das, Sachin Shivakumar, Matthew Peet, Siep Weiland

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

Abstract

This paper presents a computational framework for analyzing stability and performance of uncertain Partial Differential Equations (PDEs) when they are coupled with uncertain Ordinary Differential Equations (ODEs). To analyze the behavior of the interconnected ODE-PDE systems under uncertainty, we introduce a class of multipliers of Partial Integral (PI) operator type and consider various classes of uncertainties by enforcing constraints on these multipliers. Since the ODE-PDE models are equivalent to Partial Integral Equations (PIEs), we show that the robust stability and performance can be formulated as Linear PI Inequalities (LPIs) and LPIs can be solved by LMIs using PIETOOLS. The methods are demonstrated on examples of ODE-PDE systems that are subjected to wide classes of uncertainty.

Original languageEnglish (US)
Title of host publication2020 59th IEEE Conference on Decision and Control, CDC 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages634-639
Number of pages6
ISBN (Electronic)9781728174471
DOIs
StatePublished - Dec 14 2020
Event59th IEEE Conference on Decision and Control, CDC 2020 - Virtual, Jeju Island, Korea, Republic of
Duration: Dec 14 2020Dec 18 2020

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2020-December
ISSN (Print)0743-1546

Conference

Conference59th IEEE Conference on Decision and Control, CDC 2020
Country/TerritoryKorea, Republic of
CityVirtual, Jeju Island
Period12/14/2012/18/20

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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