State uncertainty propagation in the presence of parametric uncertainty and additive white noise

Umamaheswara Kond, Puneet Singla, Tarunraj Singh, Peter Scott

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We present a new approach to describe the evolution of uncertainty in linear dynamic models with parametric and initial condition uncertainties, and driven by additive white Gaussian stochastic forcing. This is based on the polynomial chaos (PC) series expansion of second order random processes, which has been used in several domains to solve stochastic systems with parametric and initial condition uncertainties. The PC solution is found to be an accurate approximation to ground truth, established by Monte Carlo simulation, while offering an efficient computational approach for large systems with a relatively small number of uncertainties. However, when the dynamic system includes an additive stochastic forcing term varying with time, the computational cost of using the PC expansions for the stochastic forcing terms is expensive and increases exponentially with the increase in the number of time steps, due to the increase in the stochastic dimensionality. In this work, an alternative approach is proposed for uncertainty evolution in linear uncertain models driven by white noise. The uncertainty in the model states due to additive white Gaussian noise can be described by the mean and covariance of the states. This is combined with the PC based approach to propagate the uncertainty due to Gaussian stochastic forcing and model parameter uncertainties which can be non-Gaussian.

Original languageEnglish (US)
Title of host publicationProceedings of the 2010 American Control Conference, ACC 2010
Pages3118-3123
Number of pages6
StatePublished - Oct 15 2010
Event2010 American Control Conference, ACC 2010 - Baltimore, MD, United States
Duration: Jun 30 2010Jul 2 2010

Publication series

NameProceedings of the 2010 American Control Conference, ACC 2010

Other

Other2010 American Control Conference, ACC 2010
CountryUnited States
CityBaltimore, MD
Period6/30/107/2/10

Fingerprint

White noise
Chaos theory
Polynomials
Uncertainty
Stochastic systems
Random processes
Dynamic models
Dynamical systems
Costs

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering

Cite this

Kond, U., Singla, P., Singh, T., & Scott, P. (2010). State uncertainty propagation in the presence of parametric uncertainty and additive white noise. In Proceedings of the 2010 American Control Conference, ACC 2010 (pp. 3118-3123). [5531048] (Proceedings of the 2010 American Control Conference, ACC 2010).
Kond, Umamaheswara ; Singla, Puneet ; Singh, Tarunraj ; Scott, Peter. / State uncertainty propagation in the presence of parametric uncertainty and additive white noise. Proceedings of the 2010 American Control Conference, ACC 2010. 2010. pp. 3118-3123 (Proceedings of the 2010 American Control Conference, ACC 2010).
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Kond, U, Singla, P, Singh, T & Scott, P 2010, State uncertainty propagation in the presence of parametric uncertainty and additive white noise. in Proceedings of the 2010 American Control Conference, ACC 2010., 5531048, Proceedings of the 2010 American Control Conference, ACC 2010, pp. 3118-3123, 2010 American Control Conference, ACC 2010, Baltimore, MD, United States, 6/30/10.

State uncertainty propagation in the presence of parametric uncertainty and additive white noise. / Kond, Umamaheswara; Singla, Puneet; Singh, Tarunraj; Scott, Peter.

Proceedings of the 2010 American Control Conference, ACC 2010. 2010. p. 3118-3123 5531048 (Proceedings of the 2010 American Control Conference, ACC 2010).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Kond U, Singla P, Singh T, Scott P. State uncertainty propagation in the presence of parametric uncertainty and additive white noise. In Proceedings of the 2010 American Control Conference, ACC 2010. 2010. p. 3118-3123. 5531048. (Proceedings of the 2010 American Control Conference, ACC 2010).