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 - Funding Information:
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.
Publisher Copyright:
© 2020 IEEE.
PY - 2020/12/14
Y1 - 2020/12/14
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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U2 - 10.1109/CDC42340.2020.9303892
DO - 10.1109/CDC42340.2020.9303892
M3 - Conference contribution
AN - SCOPUS:85099875444
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 634
EP - 639
BT - 2020 59th IEEE Conference on Decision and Control, CDC 2020
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 59th IEEE Conference on Decision and Control, CDC 2020
Y2 - 14 December 2020 through 18 December 2020
ER -