Lyapunov Function Construction using Constrained Least Square Optimization

Muhammad Wasim; Desineni Subbaram Naidu

doi:10.1109/IECON49645.2022.9968442

Lyapunov Function Construction using Constrained Least Square Optimization

Muhammad Wasim, Desineni Subbaram Naidu

Electrical Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

2 Scopus citations

Abstract

In this study, the Lyapunov function is constructed for polynomial dynamical systems using Constrained Least Square Optimization. In literature, the least square method is used to determine the coefficients of the Lyapunov function to make its derivative negative semi-definite. Then the coefficients are inserted in the Lyapunov function to check its positive definiteness. This way requires many iterations for finding the Lyapunov function. However, in the proposed method, a single optimization program is used to search the optimal coefficients to make the Lyapunov function positive definite and its derivative negative semi-definite. In the proposed method the polynomial Lyapunov function of a particular degree is selected with unknown coefficients. The least-square problem is solved to ensure that the coefficients of monomials that have odd power are zero and the coefficients of monomials that have even power are positive. Moreover, the least-square problem is solved under the constraint to make the derivative of the Lyapunov function along the system trajectories negative semi-definite. The proposed method is illustrated with few examples, and the results show that it successfully identifies the Lyapunov function for globally asymptotically stable systems.

Original language	English (US)
Title of host publication	IECON 2022 - 48th Annual Conference of the IEEE Industrial Electronics Society
Publisher	IEEE Computer Society
ISBN (Electronic)	9781665480253
DOIs	https://doi.org/10.1109/IECON49645.2022.9968442
State	Published - 2022
Event	48th Annual Conference of the IEEE Industrial Electronics Society, IECON 2022 - Brussels, Belgium Duration: Oct 17 2022 → Oct 20 2022

Publication series

Name	IECON Proceedings (Industrial Electronics Conference)
Volume	2022-October

Conference

Conference	48th Annual Conference of the IEEE Industrial Electronics Society, IECON 2022
Country/Territory	Belgium
City	Brussels
Period	10/17/22 → 10/20/22

Bibliographical note

Funding Information:
The authors are thankful to the IRSIP (International Research Scholarship Initiative Program) team and Higher Education Commission of Pakistan for funding this research work and facilitating at each stage during the visit. The authors acknowledge the research facilities provided by the University of Minnesota Duluth, Duluth, Minnesota USA. Special thanks to Professor Desineni Subbaram Naidu for mentoring this research work.

Funding Information:
Higher Education Commission (HEC) of Pakistan under IRSIP Scholarship program and University of Minnesota Duluth, Duluth, USA

Publisher Copyright:
© 2022 IEEE.

Keywords

Constrained Least Square Optimization
Lyapunov
Nonlinear systems
stability
Yalmip

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10.1109/IECON49645.2022.9968442

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Lyapunov Function Construction using Constrained Least Square Optimization. / Wasim, Muhammad; Naidu, Desineni Subbaram.
IECON 2022 - 48th Annual Conference of the IEEE Industrial Electronics Society. IEEE Computer Society, 2022. (IECON Proceedings (Industrial Electronics Conference); Vol. 2022-October).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Wasim, M & Naidu, DS 2022, Lyapunov Function Construction using Constrained Least Square Optimization. in IECON 2022 - 48th Annual Conference of the IEEE Industrial Electronics Society. IECON Proceedings (Industrial Electronics Conference), vol. 2022-October, IEEE Computer Society, 48th Annual Conference of the IEEE Industrial Electronics Society, IECON 2022, Brussels, Belgium, 10/17/22. https://doi.org/10.1109/IECON49645.2022.9968442

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Lyapunov Function Construction using Constrained Least Square Optimization

Abstract

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Bibliographical note

Keywords

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