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

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005630
URN to cite this document: urn:nbn:de:bvb:703-epub-5630-6

Title data

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).

Further data

Item Type:	Preprint, postprint
Additional notes (visible to public):	erscheint in: Numerical Algebra, Control and Optimization. Bd. 2 (2012) Heft 3 . - S. 547-570
Keywords:	linear-quadratic optimal control; bang-bang control; discretization
DDC Subjects:	500 Science 500 Science > 510 Mathematics
Institutions of the University:	Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne Profile Fields > Advanced Fields > Nonlinear Dynamics Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) Profile Fields Profile Fields > Advanced Fields
Language:	English
Originates at UBT:	Yes
URN:	urn:nbn:de:bvb:703-epub-5630-6
Date Deposited:	28 May 2021 09:48
Last Modified:	07 Jun 2021 11:52
URI:	https://epub.uni-bayreuth.de/id/eprint/5630

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