Uncertainty propagation with Semidefinite Programming

Hyungjin Choi; Peter J. Seiler; Sairaj V. Dhople

doi:10.1109/CDC.2015.7403157

Uncertainty propagation with Semidefinite Programming

Hyungjin Choi, Peter J. Seiler, Sairaj V. Dhople

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

3 Scopus citations

Abstract

This paper outlines an optimization-based method to estimate the reach set of a system while acknowledging unknown-but-bounded input and parametric uncertainty in the underlying dynamical model. The approach is grounded in a second-order Taylor-series expansion of the system's state variables along the solution trajectories as a function of the uncertain elements. Subsequently, over the time horizon of interest, Quadratically Constrained Quadratic Programs (QCQPs) are formulated to estimate maximum and minimum bounds on the state variables to recover the reach set. To contend with the nonconvexity of the QCQPs, Lagrangian relaxations are leveraged to formulate Semidefinite Programs (SDPs) that provide guaranteed bounds to the solutions of the QCQPs. Applications of the method to quantify the impact of uncertain power injections in power-system dynamic models are demonstrated with numerical examples.

Original language	English (US)
Title of host publication	54rd IEEE Conference on Decision and Control,CDC 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	5966-5971
Number of pages	6
ISBN (Electronic)	9781479978861
DOIs	https://doi.org/10.1109/CDC.2015.7403157
State	Published - Feb 8 2015
Event	54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan Duration: Dec 15 2015 → Dec 18 2015

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	54rd IEEE Conference on Decision and Control,CDC 2015
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Other

Other	54th IEEE Conference on Decision and Control, CDC 2015
Country/Territory	Japan
City	Osaka
Period	12/15/15 → 12/18/15

Bibliographical note

Publisher Copyright:
© 2015 IEEE.

Keywords

Quadratically Constrained Quadratic Programming
Reachability analysis
Semidefinite Programming
Sensitivity analysis
Uncertainty propagation

Publisher link

10.1109/CDC.2015.7403157

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Choi, H., Seiler, P. J., & Dhople, S. V. (2015). Uncertainty propagation with Semidefinite Programming. In 54rd IEEE Conference on Decision and Control,CDC 2015 (pp. 5966-5971). Article 7403157 (Proceedings of the IEEE Conference on Decision and Control; Vol. 54rd IEEE Conference on Decision and Control,CDC 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2015.7403157

Uncertainty propagation with Semidefinite Programming. / Choi, Hyungjin; Seiler, Peter J.; Dhople, Sairaj V.
54rd IEEE Conference on Decision and Control,CDC 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 5966-5971 7403157 (Proceedings of the IEEE Conference on Decision and Control; Vol. 54rd IEEE Conference on Decision and Control,CDC 2015).

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

Choi, H, Seiler, PJ & Dhople, SV 2015, Uncertainty propagation with Semidefinite Programming. in 54rd IEEE Conference on Decision and Control,CDC 2015., 7403157, Proceedings of the IEEE Conference on Decision and Control, vol. 54rd IEEE Conference on Decision and Control,CDC 2015, Institute of Electrical and Electronics Engineers Inc., pp. 5966-5971, 54th IEEE Conference on Decision and Control, CDC 2015, Osaka, Japan, 12/15/15. https://doi.org/10.1109/CDC.2015.7403157

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Uncertainty propagation with Semidefinite Programming

Abstract

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