American Institute of Mathematical Sciences

2012, 2(3): 547-570. doi: 10.3934/naco.2012.2.547

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

 1 Institut für Angewandte Mathematik, Friedrich-Schiller-Universität Jena, 07740 Jena, Germany 2 Mathematisches Institut, Universität Bayreuth, 95440 Bayreuth, Germany, Germany 3 Institut für Mathematik und Rechneranwendung, Fakultät für Luft- und Raumfahrttechnik, Universität der Bundeswehr, 85577 Neubiberg/München, Germany

Received  July 2011 Revised  May 2012 Published  August 2012

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 $O(h)$.
Citation: Walter Alt, Robert Baier, Matthias Gerdts, Frank Lempio. Error bounds for Euler approximation of linear-quadratic control problems with bang-bang solutions. Numerical Algebra, Control & Optimization, 2012, 2 (3) : 547-570. doi: 10.3934/naco.2012.2.547
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