A decomposition scheme for the Hamilton-Jacobi equation

Abstract

One way to compute optimal control in completely observable stochastic optimal control problems is to solve the Hamilton-Jacobi Equation. We propose to replace in the quasi linearization technique of Bellman [1] the step of inversion of a linear system of dimension n by several steps of n linear equations of dimension 1 in parallel or in sequence. We are then led to apply for instance splitting up methods-studied in particular in [3], [6], [8], [9]. We obtain what we call a decomposition scheme to approximate evolutive Hamilton-Jacobi Equation. We study convergence results as time steps converge to zero with compacity methods adapted from [4] and give some numerical results.