Certain Analysis for Uncertain Systems

Computational and Applied Mathematics Colloquium

Meeting Details

For more information about this meeting, contact Kristin Berrigan, John Harlim.

Speaker: Puneet Singla, Penn State Aerospace

Abstract: The main difficulty in the understanding of complex physical dynamic systems is due to uncertainties in the models and measurements. These systems are often studied via numerical simulations with very high dimensional input parameter space. The most critical challenge here is to provide a quantitative assessment of how closely these simulations reflect reality in the presence of model uncertainty, discretization errors, as well as measurement errors. These issues affect the way in which models are constructed, how models are used for performance analysis, and how data is integrated with models for prediction. This talk will summarize various on-going research activities at CASS (Control & Analysis of Stochastic Systems) lab at the Pennsylvania State University (PSU). The primarily focus of on-going research in CASS lab is on the development of a computationally tractable dynamic data driven framework to address challenges associated with accurate modeling, forecasting and control of engineering systems under uncertainty. These research challenges include developing non-parametric models from data, characterizing errors associated with models, propagating non-Gaussian uncertainties for large scale nonlinear systems, assimilating high dimensional noisy data with forecast model states, and incorporating the next generation of mobile sensors (such as drones) as big data collection and processing units. This talk will introduce our work on the solution of Kolmogorov equation for the evolution of state density function through nonlinear dynamical system and “optimal” quadrature methods to compute multi-dimension expectation integrals. The crux of the work lies in accounting for uncertainties in dynamical system models, characterizing the evolution of the uncertainty of the system state, and integrating disparate sources of sensor data with the model output using a Bayesian framework. By accurately characterizing the uncertainty associated with both process and measurement models, this work offers systematic design of low-complexity model-data fusion, data association and dynamic sensing algorithms with significant improvement in nominal performance and computational effort. The applicability and feasibility of these new ideas will be demonstrated on benchmark problems and some real-world problems such as tracking resident space objects (RSOs), forecasting volcano ash footprints, geo-magnetic field survey, and control of robotic systems.

Room Reservation Information

Room Number: 114 McAllister

Date: 10/28/2019

Time: 12:20pm - 1:30pm