Rapid Numerical Solution of Hamilton-Jacobi Equations in Stable Manifold Method

Abstract

This paper proposes an error estimation of a numerical method for solving Hamilton-Jacobi equations of nonlinear optimal control problems, called stable manifold method. Then, a rapid numerical algorithm is derived from the estimation. In the algorithm, the convergent sequence with respect to solutions on stable manifolds that are equivalent to the pair of optimal feedback gains and trajectories is improved. The new algorithm has three advantages, rapid calculation, extended radius of convergence and low memory consumption.