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

2 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, Jeju Island, Korea, Republic of Duration: 14 Dec 2020 → 18 Dec 2020 Conference number: 59 https://cdc2020.ieeecss.org/

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2020-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

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/

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10.1109/CDC42340.2020.9303892

Cite this

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) (pp. 634-639). [9303892] (Proceedings of the IEEE Conference on Decision and Control; Vol. 2020-December). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CDC42340.2020.9303892

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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",

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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, Proceedings of the IEEE Conference on Decision and Control, vol. 2020-December, 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 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2020-December).

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

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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.

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

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