Conjugate unscented transform-based approach to solve the fokker-planck-kolmogorov equation

Michael Mercurio, Puneet Singla

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

1 Scopus citations

Abstract

This paper presents a new approach to solve the Fokker-Planck-Kolmogorov Equation (FPKE). The main purpose of this research is to provide a method-ology to efficiently determine the time-varying state probability density function (PDF) for a general nonlinear system. Collocation-based methods often rely on high order cubature points, and require a large number of basis functions to accurately determine the solution of a partial differential equation. The recently developed Conjugate Unscented Transform is there-fore proposed to provide a minimal set of collocation points. In conjunction with this minimal cubature point method, by employing an l1 norm minimization to optimally select the appropriate basis functions from the larger complete dictionary of polynomial basis functions, a minimal polynomial expression for the state PDF is obtained at each time step.

Original languageEnglish (US)
Title of host publicationAIAA/AAS Astrodynamics Specialist Conference, 2016
PublisherAmerican Institute of Aeronautics and Astronautics Inc, AIAA
ISBN (Print)9781624104459
Publication statusPublished - Jan 1 2016
EventAIAA/AAS Astrodynamics Specialist Conference, 2016 - Long Beach, United States
Duration: Sep 13 2016Sep 16 2016

Publication series

NameAIAA/AAS Astrodynamics Specialist Conference, 2016

Other

OtherAIAA/AAS Astrodynamics Specialist Conference, 2016
CountryUnited States
CityLong Beach
Period9/13/169/16/16

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All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Aerospace Engineering

Cite this

Mercurio, M., & Singla, P. (2016). Conjugate unscented transform-based approach to solve the fokker-planck-kolmogorov equation. In AIAA/AAS Astrodynamics Specialist Conference, 2016 (AIAA/AAS Astrodynamics Specialist Conference, 2016). American Institute of Aeronautics and Astronautics Inc, AIAA.