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On the convergence of the gradient projection method for convex optimal control problems with bang–bang solutions

On the convergence of the gradient projection method for convex optimal control problems with bang–bang solutions
On the convergence of the gradient projection method for convex optimal control problems with bang–bang solutions
We revisit the gradient projection method in the framework of nonlinear optimal control problems with bang–bang solutions. We obtain the strong convergence of the iterative sequence of controls and the corresponding trajectories. Moreover, we establish a convergence rate, depending on a constant appearing in the corresponding switching function and prove that this convergence rate estimate is sharp. Some numerical illustrations are reported confirming the theoretical results.
0926-6003
221-238
Preininger, J.
f8b96f14-7403-494c-9ff2-e615f008ab03
Vuong, P. T.
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf
Preininger, J.
f8b96f14-7403-494c-9ff2-e615f008ab03
Vuong, P. T.
52577e5d-ebe9-4a43-b5e7-68aa06cfdcaf

Preininger, J. and Vuong, P. T. (2018) On the convergence of the gradient projection method for convex optimal control problems with bang–bang solutions. Computational Optimization and Applications, 70 (1), 221-238. (doi:10.1007/s10589-018-9981-6).

Record type: Article

Abstract

We revisit the gradient projection method in the framework of nonlinear optimal control problems with bang–bang solutions. We obtain the strong convergence of the iterative sequence of controls and the corresponding trajectories. Moreover, we establish a convergence rate, depending on a constant appearing in the corresponding switching function and prove that this convergence rate estimate is sharp. Some numerical illustrations are reported confirming the theoretical results.

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e-pub ahead of print date: 29 January 2018
Published date: 1 May 2018

Identifiers

Local EPrints ID: 434645
URI: http://eprints.soton.ac.uk/id/eprint/434645
DOI: doi:10.1007/s10589-018-9981-6
ISSN: 0926-6003
PURE UUID: d8d5f341-44d9-4913-9a29-6d8e9c5c6925
ORCID for P. T. Vuong: ORCID iD orcid.org/0000-0002-1474-994X

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Date deposited: 04 Oct 2019 16:30
Last modified: 16 Mar 2024 04:42

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Contributors

Author: J. Preininger
Author: P. T. Vuong ORCID iD

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