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

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


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