Joe Imae and Kenjiro Shinagawa and Tomoaki Kobayashi and Guisheng Zhai
A New Approach to the Approximate Solutions of HamiltonJacobi Equations
437 - 440
2011
5
3
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/14467
https://publications.waset.org/vol/51
World Academy of Science, Engineering and Technology
We propose a new approach on how to obtain the approximate solutions of HamiltonJacobi (HJ) equations. The process of the approximation consists of two steps. The first step is to transform the HJ equations into the virtual time based HJ equations (VTHJ) by introducing a new idea of ‘virtualtime’. The second step is to construct the approximate solutions of the HJ equations through a computationally iterative procedure based on the VTHJ equations. It should be noted that the approximate feedback solutions evolve by themselves as the virtualtime goes by. Finally, we demonstrate the effectiveness of our approximation approach by means of simulations with linear and nonlinear control problems.
Open Science Index 51, 2011