The Euler Method for Linear Control Systems Revisited

Abstract : Although optimal control problems for linear systems have been profoundly investigated in the past 50-60 years, the issue of numerical approximations and precise error analyses remains challenging due the bang-bang structure of the optimal controls. Based on a recent paper by M. Quincampoix and V.M. Veliov on metric regularity of the optimality conditions for control problems of linear systems the paper presents new error estimates for the Euler discretization scheme applied to such problems. It turns out that the accuracy of the Euler method depends on the "controllability index" associated with the optimal solution, and a sharp error estimate is given in terms of this index. The result extends and strengthens in several directions some recently published ones.
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Contributor : Alain Pietrus <>
Submitted on : Friday, May 30, 2014 - 3:05:31 PM
Last modification on : Wednesday, December 19, 2018 - 1:08:13 PM

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Alain Pietrus, Vladimir Veliov, Josef Haunschmied. The Euler Method for Linear Control Systems Revisited. 9-th International Conference, LSSC 2013, 2013, Sozopol, Bulgaria. 8353, pp.88-95, 2014. 〈hal-00998121〉

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