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

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Alt, Walter ; Baier, Robert ; Gerdts, Matthias ; Lempio, Frank:
Error bounds for Euler approximation of linear-quadratic control problems with bang-bang solutions.
Bayreuth , 2011

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Abstract

We analyze the Euler discretization to a class of linear 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 obtan an error estimate of order O(h).