Estimating Regions of Attraction for Transitional Flows Using Quadratic Constraints

Aniketh Kalur; Talha Mushtaq; Peter J Seiler Jr; Maziar S. Hemati

doi:10.1109/LCSYS.2021.3081382

Estimating Regions of Attraction for Transitional Flows Using Quadratic Constraints

Aniketh Kalur, Talha Mushtaq, Peter J Seiler Jr, Maziar S. Hemati

Aerospace Engineering and Mechanics

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

This letter describes a method for estimating regions of attraction and bounds on permissible perturbation amplitudes in nonlinear fluids systems. The proposed approach exploits quadratic constraints between the inputs and outputs of the nonlinearity on elliptical sets. This approach reduces conservatism and improves estimates for regions of attraction and bounds on permissible perturbation amplitudes over related methods that employ quadratic constraints on spherical sets. We present and investigate two algorithms for performing the analysis: an iterative method that refines the analysis by solving a sequence of semi-definite programs, and another based on solving a generalized eigenvalue problem with lower computational complexity, but at the cost of some precision in the final solution. The proposed algorithms are demonstrated on low-order mechanistic models of transitional flows. We further compare accuracy and computational complexity with analysis based on sum-of-squares optimization and direct-adjoint looping methods.

Original language	English (US)
Article number	9432939
Pages (from-to)	482-487
Number of pages	6
Journal	IEEE Control Systems Letters
Volume	6
DOIs	https://doi.org/10.1109/LCSYS.2021.3081382
State	Published - 2022

Bibliographical note

Funding Information:
Manuscript received March 4, 2021; revised May 7, 2021; accepted May 11, 2021. Date of publication May 17, 2021; date of current version June 25, 2021. This work was supported by Army Research Office under Grant W911NF-20-1-0156. The work of Maziar S. Hemati was supported in part by the Air Force Office of Scientific Research under Award FA 9550-19-1-0034, and in part by the National Science Foundation under Grant CBET-1943988. Recommended by Senior Editor C. Prieur. (Corresponding author: Maziar S. Hemati.) Aniketh Kalur, Talha Mushtaq, and Maziar S. Hemati are with the Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455 USA (e-mail: [email protected]).

Publisher Copyright:
© 2017 IEEE.

Keywords

Region of attraction
quadratic constraints
transitional fluid flows

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10.1109/LCSYS.2021.3081382

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abstract = "This letter describes a method for estimating regions of attraction and bounds on permissible perturbation amplitudes in nonlinear fluids systems. The proposed approach exploits quadratic constraints between the inputs and outputs of the nonlinearity on elliptical sets. This approach reduces conservatism and improves estimates for regions of attraction and bounds on permissible perturbation amplitudes over related methods that employ quadratic constraints on spherical sets. We present and investigate two algorithms for performing the analysis: an iterative method that refines the analysis by solving a sequence of semi-definite programs, and another based on solving a generalized eigenvalue problem with lower computational complexity, but at the cost of some precision in the final solution. The proposed algorithms are demonstrated on low-order mechanistic models of transitional flows. We further compare accuracy and computational complexity with analysis based on sum-of-squares optimization and direct-adjoint looping methods.",

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note = "Funding Information: Manuscript received March 4, 2021; revised May 7, 2021; accepted May 11, 2021. Date of publication May 17, 2021; date of current version June 25, 2021. This work was supported by Army Research Office under Grant W911NF-20-1-0156. The work of Maziar S. Hemati was supported in part by the Air Force Office of Scientific Research under Award FA 9550-19-1-0034, and in part by the National Science Foundation under Grant CBET-1943988. Recommended by Senior Editor C. Prieur. (Corresponding author: Maziar S. Hemati.) Aniketh Kalur, Talha Mushtaq, and Maziar S. Hemati are with the Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455 USA (e-mail: [email protected]). Publisher Copyright: {\textcopyright} 2017 IEEE.",

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N2 - This letter describes a method for estimating regions of attraction and bounds on permissible perturbation amplitudes in nonlinear fluids systems. The proposed approach exploits quadratic constraints between the inputs and outputs of the nonlinearity on elliptical sets. This approach reduces conservatism and improves estimates for regions of attraction and bounds on permissible perturbation amplitudes over related methods that employ quadratic constraints on spherical sets. We present and investigate two algorithms for performing the analysis: an iterative method that refines the analysis by solving a sequence of semi-definite programs, and another based on solving a generalized eigenvalue problem with lower computational complexity, but at the cost of some precision in the final solution. The proposed algorithms are demonstrated on low-order mechanistic models of transitional flows. We further compare accuracy and computational complexity with analysis based on sum-of-squares optimization and direct-adjoint looping methods.

AB - This letter describes a method for estimating regions of attraction and bounds on permissible perturbation amplitudes in nonlinear fluids systems. The proposed approach exploits quadratic constraints between the inputs and outputs of the nonlinearity on elliptical sets. This approach reduces conservatism and improves estimates for regions of attraction and bounds on permissible perturbation amplitudes over related methods that employ quadratic constraints on spherical sets. We present and investigate two algorithms for performing the analysis: an iterative method that refines the analysis by solving a sequence of semi-definite programs, and another based on solving a generalized eigenvalue problem with lower computational complexity, but at the cost of some precision in the final solution. The proposed algorithms are demonstrated on low-order mechanistic models of transitional flows. We further compare accuracy and computational complexity with analysis based on sum-of-squares optimization and direct-adjoint looping methods.

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Estimating Regions of Attraction for Transitional Flows Using Quadratic Constraints

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