Convergence analysis of Euler discretization of control-state constrained optimal control problems with controls of bounded variation

Matthias Gerdts; Martin Kunkel

doi:10.3934/jimo.2014.10.311

Article Contents

2014, Volume 10, Issue 1: 311-336. Doi: 10.3934/jimo.2014.10.311

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Convergence analysis of Euler discretization of control-state constrained optimal control problems with controls of bounded variation

Matthias Gerdts^1, and
Martin Kunkel^2,

1.
Universität der Bundeswehr München, Institut für Mathematik und Rechneranwendung, Werner-Heisenberg-Weg 39, 85577 Neubiberg
2.
Elektrobit Automotive GmbH, Am Wolfsmantel 46, 91058 Erlangen

Received: September 30, 2012

Revised: June 30, 2013

Published: December 2013

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Abstract

We study convergence properties of Euler discretization of optimal control problems with ordinary differential equations and mixed control-state constraints. Under suitable consistency and stability assumptions a convergence rate of order $1/p$ of the discretized control to the continuous control is established in the $L^p$-norm. Throughout it is assumed that the optimal control is of bounded variation. The convergence proof exploits the reformulation of first order necessary optimality conditions as nonsmooth equations.

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Mathematics Subject Classification: Primary: 49J15, 49J52, 49M25; Secondary: 49K40.

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References

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