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Error bounds for Euler approximation of linear-quadratic control problems with bang-bang solutions

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  • We analyze the Euler discretization to a class of linear-quadratic optimal control problems. First we show convergence of order $h$ for the optimal values of the objective function, where $h$ is the mesh size. Under the additional assumption that the optimal control has bang-bang structure we show that the discrete and the continuous controls coincide except on a set of measure $O(\sqrt{h})$. Under a slightly stronger assumption on the smoothness of the coefficients of the system equation we obtain an error estimate of order $O(h)$.
    Mathematics Subject Classification: Primary: 49J15; Secondary: 49M25, 49N10, 49J30.

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