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

Amritam Das; Sachin Shivakumar; Matthew Peet; Siep Weiland

doi:10.1109/CDC42340.2020.9303892

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 proceeding › Conference contribution › Academic › peer-review

6 Citations (Scopus)

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 language	English
Title of host publication	59th IEEE Conference on Decision and Control (CDC 2020)
Publisher	Institute of Electrical and Electronics Engineers
Pages	634-639
Number of pages	6
ISBN (Electronic)	978-1-7281-7447-1
DOIs	https://doi.org/10.1109/CDC42340.2020.9303892
Publication status	Published - 11 Jan 2021
Event	59th IEEE Conference on Decision and Control, CDC 2020 - Virtual/Online, Virtual, Jeju Island, Korea, Republic of Duration: 14 Dec 2020 → 18 Dec 2020 Conference number: 59 https://cdc2020.ieeecss.org/

Conference

Conference	59th IEEE Conference on Decision and Control, CDC 2020
Abbreviated title	CDC
Country/Territory	Korea, Republic of
City	Virtual, Jeju Island
Period	14/12/20 → 18/12/20
Internet address	https://cdc2020.ieeecss.org/

Funding

Acknowledgment: This work was supported by Office of Naval Research Award N00014-17-1-2117, and National Science Foundation grants CMMI-1935453 and CNS-1739990.

Access to Document

10.1109/CDC42340.2020.9303892

Cite this

@inproceedings{98bd20b637c14bca86e947e67b83159d,

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

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.",

author = "Amritam Das and Sachin Shivakumar and Matthew Peet and Siep Weiland",

year = "2021",

month = jan,

day = "11",

doi = "10.1109/CDC42340.2020.9303892",

language = "English",

pages = "634--639",

booktitle = "59th IEEE Conference on Decision and Control (CDC 2020)",

publisher = "Institute of Electrical and Electronics Engineers",

address = "United States",

note = "59th IEEE Conference on Decision and Control, CDC 2020, CDC ; Conference date: 14-12-2020 Through 18-12-2020",

url = "https://cdc2020.ieeecss.org/",

}

Das, A, Shivakumar, S, Peet, M & Weiland, S 2021, Robust Analysis of Uncertain ODE-PDE Systems Using PI Multipliers, PIEs and LPIs. in 59th IEEE Conference on Decision and Control (CDC 2020)., 9303892, Institute of Electrical and Electronics Engineers, pp. 634-639, 59th IEEE Conference on Decision and Control, CDC 2020, Virtual, Jeju Island, Korea, Republic of, 14/12/20. https://doi.org/10.1109/CDC42340.2020.9303892

Robust Analysis of Uncertain ODE-PDE Systems Using PI Multipliers, PIEs and LPIs. / Das, Amritam; Shivakumar, Sachin; Peet, Matthew et al.
59th IEEE Conference on Decision and Control (CDC 2020). Institute of Electrical and Electronics Engineers, 2021. p. 634-639 9303892.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Robust Analysis of Uncertain ODE-PDE Systems Using PI Multipliers, PIEs and LPIs

AU - Das, Amritam

AU - Shivakumar, Sachin

AU - Peet, Matthew

AU - Weiland, Siep

N1 - Conference code: 59

PY - 2021/1/11

Y1 - 2021/1/11

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85099875444&partnerID=8YFLogxK

U2 - 10.1109/CDC42340.2020.9303892

DO - 10.1109/CDC42340.2020.9303892

M3 - Conference contribution

AN - SCOPUS:85099875444

SP - 634

EP - 639

BT - 59th IEEE Conference on Decision and Control (CDC 2020)

PB - Institute of Electrical and Electronics Engineers

T2 - 59th IEEE Conference on Decision and Control, CDC 2020

Y2 - 14 December 2020 through 18 December 2020

ER -

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

Abstract

Conference

Funding

Access to Document

Other files and links

Fingerprint

Cite this