Uncertainty propagation with Semidefinite Programming

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish (US)
Title of host publication54rd IEEE Conference on Decision and Control,CDC 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5966-5971
Number of pages6
ISBN (Electronic)9781479978861
DOIs
StatePublished - Feb 8 2015
Event54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan
Duration: Dec 15 2015Dec 18 2015

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume54rd IEEE Conference on Decision and Control,CDC 2015
ISSN (Print)0743-1546

Other

Other54th IEEE Conference on Decision and Control, CDC 2015
CountryJapan
CityOsaka
Period12/15/1512/18/15

Keywords

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

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