@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}, }