Approximate Solutions to Hamilton-Jacobi Equations Based on Chebyshev Polynomials

In this paper, we propose a new approximate solution to a Hamilton-Jacobi equation used in nonlinear optimal control. First, the Galerkin approximation with Chebyshev polynomials is applied to Hamilton-Jacobi equations. Second, it is proved that the computational effort of the proposed algorithm is less than the existing one. Finally, a numerical example shows the effectiveness of the proposed method.