| Many of the theoretical results in nonlinear optimal control and H-infinity theory depend on the solution of a Hamilton-Jacobi equation, a first order nonlinear partial differential equation. Unfortunately, in general these equations cannot be solved analytically, which limits the applicability of the theory to real world problems. In this thesis, an iterative procedure is introduced which solves numerically this first-order nonlinear equation. Proofs are given which insure convergence to the unique stabilizing solution of the H-J equation, and convergence is shown to be exponential with respect to the iteration variable. The algorithm is implemented on a number of illustrative and comparative examples. |
