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The Euler approximation in state constrained optimal control


Authors: A. L. Dontchev and William W. Hager
Journal: Math. Comp. 70 (2001), 173-203
MSC (2000): Primary 49M25, 65L10, 65L70, 65K10
DOI: https://doi.org/10.1090/S0025-5718-00-01184-4
Published electronically: April 13, 2000
MathSciNet review: 1681116
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Abstract:

We analyze the Euler approximation to a state constrained control problem. We show that if the active constraints satisfy an independence condition and the Lagrangian satisfies a coercivity condition, then locally there exists a solution to the Euler discretization, and the error is bounded by a constant times the mesh size. The proof couples recent stability results for state 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 invoked.


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Additional Information

A. L. Dontchev
Affiliation: Mathematical Reviews, Ann Arbor, Michigan 48107
Email: ald@ams.org

William W. Hager
Affiliation: Department of Mathematics, University of Florida, Gainesville, Florida 32611
Email: hager@math.ufl.edu

DOI: https://doi.org/10.1090/S0025-5718-00-01184-4
Keywords: Optimal control, state constraints, Euler discretization, error estimates, variational inequality
Received by editor(s): October 15, 1998
Received by editor(s) in revised form: February 16, 1999
Published electronically: April 13, 2000
Additional Notes: This research was supported by the National Science Foundation.
Article copyright: © Copyright 2000 American Mathematical Society