A new approach to the approximate solutions of Hamilton-Jacobi equations

Joe Imae, Kenjiro Shinagawa, Tomoaki Kobayashi, Guisheng Zhai

Research output: Contribution to journalArticlepeer-review

Abstract

We propose a new approach on how to obtain the approximate solutions of Hamilton-Jacobi (HJ) equations. The process of the approximation consists of two steps. The first step is to transform the standard HJ equations into the virtual time based HJ equations (VT-HJ) by introducing a new idea of 'virtual-time'. The second step is to construct the approximate solutions of the HJ equations through a computationally iterative procedure based on the VT-HJ equations. It should be noted that the approximate feedback solutions evolve by themselves as the virtual-time goes by. Finally, we demonstrate the effectiveness of our approximation approach by means of simulations with linear and nonlinear control problems.

Original languageEnglish
Pages (from-to)313-316
Number of pages4
JournalWorld Academy of Science, Engineering and Technology
Volume75
Publication statusPublished - 2011 Mar 1

Keywords

  • Hamilton-Jacobi equation
  • Nonlinear control
  • Optimal control
  • Virtual-time

ASJC Scopus subject areas

  • Engineering(all)

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