Numerical results for a product formula approximation of Hamilton-Jacobi equations

Abstract

The numerical approximation of the Hamilton-Jacobi equation associated to an optimal control problem is considered by use of a fractional steps method for decoupling it. The mathematical results concerning this approximation scheme ar£ presented. Numerical algorithms with different variants are developed for ID and 2D problems to compute (sub)optimal feedback controls. Numerical tests are presented showing that this approximation method yields a numerically workable procedure to solve Hamilton-Jacobi equations.

Keywords:

• Optimal control problem
• feedback optimal control
• Hamilton-Jacobi equation
• fractional steps method

C.R. Categories:

• G.1.8
• G.1.6