Research Summaries

Back Numerical Solution of First Order Partial Differential Equations of Nonlinear Control

Fiscal Year 2011
Division Graduate School of Engineering & Applied Science
Department Applied Mathematics
Investigator(s) Krener, Arthur J.
Sponsor Air Force Office of Scientific Research (Air Force)
Summary There are two types of first order partial differential equations that arise over and over again in many algorithms for the control and estimation of nonlinear systems. These types are the Hamilton Jacobi Bellman PDEs (HJB PDEs) and Intertwining PDEs (ITW PDEs). Solutions to one or both these PDEs are essential parts of many algorithms for nonlinear control and estimation yet there are few effective methods for their solution when the state dimension is greater than two or three.
We propose to develop new, higher order methods for solving such equations. These method will combine power series techniques, Cauchy-Kovalevskaya techniques, patchy techniques, fast sweeping methods and fast marching methods.
Keywords
Publications Publications, theses (not shown) and data repositories will be added to the portal record when information is available in FAIRS and brought back to the portal
Data Publications, theses (not shown) and data repositories will be added to the portal record when information is available in FAIRS and brought back to the portal