A Posteriori Error Estimates in Time-Domain Decomposition of Final Value Optimal Control of the Acoustic Wave Equation

A Posteriori Error Estimates in Time-Domain Decomposition of Final Value Optimal Control of the... Abstract. We consider a boundary optimal control problem for the acoustic wave equation with a final value cost criterion. A time-domain decomposition procedure for the corresponding optimality system is introduced, which leads to a sequence of uncoupled optimality systems of local-in-time optimal control problems. The process is inherently parallel and is suitable for real-time control applications. Convergence of the local solutions and controls to the global ones was established in an earlier publication. In this paper, a posteriori error estimates of the difference between the local solutions and the global one are obtained in terms of the mismatch of the n th iterates, or of successive iterates, across the time-domain break points. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

A Posteriori Error Estimates in Time-Domain Decomposition of Final Value Optimal Control of the Acoustic Wave Equation

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Publisher
Springer-Verlag
Copyright
Copyright © Inc. by 2002 Springer-Verlag New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-002-0750-6
Publisher site
See Article on Publisher Site

Abstract

Abstract. We consider a boundary optimal control problem for the acoustic wave equation with a final value cost criterion. A time-domain decomposition procedure for the corresponding optimality system is introduced, which leads to a sequence of uncoupled optimality systems of local-in-time optimal control problems. The process is inherently parallel and is suitable for real-time control applications. Convergence of the local solutions and controls to the global ones was established in an earlier publication. In this paper, a posteriori error estimates of the difference between the local solutions and the global one are obtained in terms of the mismatch of the n th iterates, or of successive iterates, across the time-domain break points.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Dec 19, 2002

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