%0 Journal Article
	%A Joe Imae and  Kenjiro Shinagawa and  Tomoaki Kobayashi and  Guisheng Zhai
	%D 2011
	%J International Journal of Mathematical and Computational Sciences
	%B World Academy of Science, Engineering and Technology
	%I Open Science Index 51, 2011
	%T A New Approach to the Approximate Solutions of Hamilton-Jacobi Equations
	%U https://publications.waset.org/pdf/14467
	%V 51
	%X 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 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.

	%P 437 - 440