Abstract
In this paper, we improve an earlier iterative successive approximation method for solving the Hamilton-Jacobi equation (HJE) arising in deterministic optimal control of affine nonlinear systems. The new methods generate smooth approximate solutions for systems with polynomial nonlinearities, compared with the former method that generates rational functions with possible singularities in the domain. We prove quadratic convergence of the methods and demonstrate their effectiveness with some examples. Application to factorisation of nonlinear systems is also discussed.