Uncertainty propagation in dynamical systems

Authors:
Igor Mezić;Thordur Runolfsson
Affiliations:
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93105-5070, United States;School of Electrical and Computer Engineering, The University of Oklahoma, Norman, OK 73019-1023, United States
Venue:
Automatica (Journal of IFAC)
Year:
2008

Citing 4
Cited 1

Stochastic finite elements: a spectral approach

Stochastic finite elements: a spectral approach
Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element approach

Physica D - Special issue originating from the 18th Annual International Conference of the Center for Nonlinear Studies, Los Alamos, NM, May 11&mdash ;15, 1998
A framework for assessing uncertainties in simulation predictions

Physica D - Special issue originating from the 18th Annual International Conference of the Center for Nonlinear Studies, Los Alamos, NM, May 11&mdash ;15, 1998
An Equation-Free, Multiscale Approach to Uncertainty Quantification

Computing in Science and Engineering

Efficient optimal design of uncertain discrete time dynamical systems

Automatica (Journal of IFAC)

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Abstract

Dynamical propagation of parametric and initial condition uncertainty is studied. The notion of input measure of an observable is defined and its propagation to output measure of the observable is studied by means of transfer operators. Uncertainty of these measures is defined in terms of their cumulative probability distributions. Comparison with alternative uncertainty metrics such as variance and entropy is pursued. The developed formalism is illustrated through an analysis of the effect of pitchfork bifurcation on uncertainty. Finally, the implications of these concepts in the design of nonlinear systems are discussed.