The Euler approximation in state constrained optimal control

Dontchev, A.; Hager, William

doi:10.1090/S0025-5718-00-01184-4

The Euler approximation in state constrained optimal control
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by A. L. Dontchev and William W. Hager;

Math. Comp. 70 (2001), 173-203

DOI: https://doi.org/10.1090/S0025-5718-00-01184-4

Published electronically: April 13, 2000

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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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