An iterative algorithm for solving Hamilton-Jacobi type equations

Citation
J. Markman et In. Katz, An iterative algorithm for solving Hamilton-Jacobi type equations, SIAM J SC C, 22(1), 2000, pp. 312-329
Citations number
10
Categorie Soggetti
Mathematics
Journal title
SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN journal
10648275 → ACNP
Volume
22
Issue
1
Year of publication
2000
Pages
312 - 329
Database
ISI
SICI code
1064-8275(20000623)22:1<312:AIAFSH>2.0.ZU;2-7
Abstract
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.