@article{(Open Science Index):https://publications.waset.org/pdf/14467,
	  title     = {A New Approach to the Approximate Solutions of Hamilton-Jacobi Equations},
	  author    = {Joe Imae and  Kenjiro Shinagawa and  Tomoaki Kobayashi and  Guisheng Zhai},
	  country	= {},
	  institution	= {},
	  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 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.
	    journal   = {International Journal of Mathematical and Computational Sciences},
	  volume    = {5},
	  number    = {3},
	  year      = {2011},
	  pages     = {437 - 440},
	  ee        = {https://publications.waset.org/pdf/14467},
	  url   	= {https://publications.waset.org/vol/51},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 51, 2011},