The Euler approximation in state constrained optimal control

Citation
Al. Dontchev et Ww. Hager, The Euler approximation in state constrained optimal control, MATH COMPUT, 70(233), 2001, pp. 173-203
Citations number
41
Categorie Soggetti
Mathematics
Journal title
MATHEMATICS OF COMPUTATION
ISSN journal
00255718 → ACNP
Volume
70
Issue
233
Year of publication
2001
Pages
173 - 203
Database
ISI
SICI code
0025-5718(200101)70:233<173:TEAISC>2.0.ZU;2-7
Abstract
We analyze the Euler approximation to a state constrained control problem. We show that if the active constraints satisfy an independence condition an d the Lagrangian satisfies a coercivity condition, then locally there exist s a solution to the Euler discretization, and the error is bounded by a con stant times the mesh size. The proof couples recent stability results for s tate constrained control problems with results established here on discrete -time regularity. The analysis utilizes mappings of the discrete variables into continuous spaces where classical finite element estimates can be invo ked.