Error Bounds for Euler Approximation of Linear-quadratic Control Problems with Bang-bang Solutions
نویسندگان
چکیده
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, 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( √ 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).
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