Second-order Runge-Kutta approximations in control constrained optimal control

Authors
Dontchev, AL Hager, WW Veliov, VM
Citation
Al. Dontchev et al., Second-order Runge-Kutta approximations in control constrained optimal control, SIAM J NUM, 38(1), 2000, pp. 202-226
Citations number
54
Categorie Soggetti
Mathematics
Journal title
SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN journal
00361429 → ACNP
Volume
38
Issue
1
Year of publication
2000
Pages
202 - 226
Database
ISI
SICI code
0036-1429(20000623)38:1<202:SRAICC>2.0.ZU;2-7
Abstract
In this paper, we analyze second-order Runge-Kutta approximations to a nonl inear optimal control problem with control constraints. If the optimal cont rol has a derivative of bounded variation and a coercivity condition holds, we show that for a special class of Runge Kutta schemes, the error in the discrete approximating control is O(h(2)) where h is the mesh spacing.