Stochastic Framework for Optimal Control of Planetary Reentry Trajectories Under Multilevel Uncertainties

Wang, Zhiheng; Ghanem, Roger

doi:10.2514/1.j062515

Stochastic Framework for Optimal Control of Planetary Reentry Trajectories Under Multilevel Uncertainties

Journal Article · Tue Aug 01 00:00:00 EDT 2023 · AIAA Journal

DOI:https://doi.org/10.2514/1.j062515· OSTI ID:2422569

^[1]; Ghanem, Roger ^[1]

University of Southern California, Los Angeles, California 90089

We present a novel stochastic optimal control framework that accounts for various types of uncertainties, with application to reentry trajectory planning. The formulation of the optimal trajectory control problem is presented in the context of an indirect method where a functional objective associated with the terminal vehicle speed is to be minimized. Uncertain input parameters in the optimal trajectory control model, including aerodynamic parameters and initial and terminal conditions, are modeled as aleatory random variables, while the statistical parameters of these aleatory distributions are themselves random variables. The parametric and model uncertainties are simultaneously propagated through an extended polynomial chaos expansion (EPCE) formalism. Several metrics are described to evaluate response statistics and presented as insightful tools for robust decision making. Specifically, the response probability density function (PDF) reflecting influence of both epistemic and aleatory uncertainties is obtained. By sampling over the random variables representing model error, an ensemble of response PDFs is generated and the associated failure probability is estimated as a random variable with its own polynomial chaos expansion. Besides, the sensitivity index functions of response PDF with respect to the statistical parameters are evaluated. Coupling parametric and model uncertainties within the EPCE framework leads to a robust and efficient paradigm for multilevel uncertainty propagation and PDF characterization in general optimal control problems.

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). FASTMath SciDAC-5 Institute

Sponsoring Organization:: USDOE

DOE Contract Number:: AC02-05CH11231

OSTI ID:: 2422569

Journal Information:: AIAA Journal, Journal Name: AIAA Journal Journal Issue: 8 Vol. 61; ISSN 0001-1452

Publisher:: AIAA

Country of Publication:: United States

Language:: English

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