# American Institute of Mathematical Sciences

January  2014, 10(1): 311-336. doi: 10.3934/jimo.2014.10.311

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

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

Received  October 2012 Revised  July 2013 Published  October 2013

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.
Citation: Matthias Gerdts, Martin Kunkel. Convergence analysis of Euler discretization of control-state constrained optimal control problems with controls of bounded variation. Journal of Industrial & Management Optimization, 2014, 10 (1) : 311-336. doi: 10.3934/jimo.2014.10.311
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