Abstract
Although optimal control problems for linear systems have been profoundly investigated in the past more than 50 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.
This research is supported by the Austrian Science Foundation (FWF) under grant No I 476-N13. The paper was written during the visit of the third author at Université des Antilles et de la Guyane, Feb., 2013.
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Haunschmied, J.L., Pietrus, A., Veliov, V.M. (2014). The Euler Method for Linear Control Systems Revisited. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2013. Lecture Notes in Computer Science(), vol 8353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-43880-0_9
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DOI: https://doi.org/10.1007/978-3-662-43880-0_9
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