Error bounds for Euler approximation of linear-quadratic control problems with bang-bang solutions
Error bounds for Euler approximation of linear-quadratic control problems with bang-bang solutions
复制标题
具有 bang-bang 解的线性二次控制问题的欧拉逼近的误差界
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
F. Lempio
中科院分区：
文献类型：
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作者：
W. Alt;Robert Baier;M. Gerdts;F. Lempio
研究了一类线性二次最优问题的欧拉离散化问题
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 $O(h)$.