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Meeting	ACGS Committee Meeting 131 - Newport News, VA - October 2023
Agenda Location	5 SUBCOMMITTEE B – MISSILES AND SPACE 5.3 Efficient Uncertainty Propagation and Optimal Feedback Control Design for Uncertain Systems
Title	Efficient Uncertainty Propagation and Optimal Feedback Control Design for Uncertain Systems
Presenter	Puneet Singla
Affiliation	Penn State
Available Downloads*	presentation
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Abstract	The main difficulty in the understanding of engineering dynamic systems is due to uncertainties in the models and measurements. These systems are often studied via numerical simulations by sampling the 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. This talk will introduce our work on the solution of Kolmogorov equation for the evolution of state probability density function (PDF) 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. These novel quadrature rules known as the Conjugate Unscented Transformation (CUT) provide the extension of celebrated “Unscented Transformation” to capture higher order moments. Furthermore, these CUT provided samples are used in conjunction with sparse approximation tools to solve the Kolmogorov equation for the state PDF and the Hamilton-Jacobi-Bellman (HJB) equation for the optimal feedback control. The approach comprises of a collocation scheme to alleviate the curse of dimensionality by employing a unique combination of non-product quadrature methods and sparse approximation tools. A salient feature of the proposed approach is its non-parametric nature, where the solution process does not assume any structure for the field variable of interest. 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) and optimal feedback control of aerospace vehicles.