An iterative algorithm for solving Hamilton-Jacobi type equations

Solutions of the optimal control and H-infinity-control problems for nonlin ear a ne systems can be found by solving Hamilton Jacobi equations. However , these first-order nonlinear partial differential equations can, in genera l, not be solved analytically. This paper introduces an iterative algorithm which solves these equations numerically for points near the origin. The p rocedure converges to the stabilizing solution exponentially with respect t o the iteration variable. The algorithm is implemented on both illustrative and comparative examples.