Uncertainty Quantification for Stochastic Nonlinear Systems using Perron-Frobenius Operator and Karhunen-Loeve Expansion Conference Paper

abstract

• In this paper, a methodology for propagation of uncertainty in stochastic nonlinear dynamical systems is investigated. The process noise is approximated using Karhunen-Love (KL) expansion. Perron-Frobenius (PF) operator is used to predict the evolution of uncertainty. A multivariate Kolmogorov-Smirnov test is used to verify the proposed framework. The method is applied to predict uncertainty evolution in a Duffing oscillator and a Vanderpol's oscillator. It is observed that the solution of the approximated stochastic dynamics converges to the true solution in distribution. Finally, the proposed methodology is combined with Bayesian inference to estimate states of a nonlinear dynamical system, and its performance is compared with particle filter. The proposed estimator was found to be computationally superior than the particle filter. 2012 IEEE.

name of conference

• 2012 IEEE International Conference on Control Applications

authors

• Bhattacharya, Raktim

published proceedings

• 2012 IEEE INTERNATIONAL CONFERENCE ON CONTROL APPLICATIONS (CCA)

author list (cited authors)

• Dutta, P., Halder, A., & Bhattacharya, R.

citation count

• 13

complete list of authors

• Dutta, Parikshit||Halder, Abhishek||Bhattacharya, Raktim

publication date

• October 2012

publisher

• Institute of Electrical and Electronics Engineers (IEEE)  Publisher

published in

• Proceedings of the IEEE Conference on Control Applications  Journal

Digital Object Identifier (DOI)

• 10.1109/cca.2012.6402455

International Standard Book Number (ISBN) 13

• 9781467345033

start page

• 1449

end page

• 1454

URL

• http%3A%2F%2Fdx.doi.org%2F10.1109%2Fcca.2012.6402455