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

Title data

Alt, Walter ; Baier, Robert ; Gerdts, Matthias ; Lempio, Frank:
Error bounds for Euler approximation of linear-quadratic control problems with bang-bang solutions.
In: Numerical Algebra, Control and Optimization. Vol. 2 (2012) Issue 3 . - pp. 547-570.
ISSN 2155-3297
DOI: https://doi.org/10.3934/naco.2012.2.547

Review:

Abstract in another language

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: Article in a journal
Refereed: Yes
Additional notes: A special issue dedicated to Professor Helmut Maurer on the occasion of his 65th birthday.

Contents:
1. Introduction
2. Euler Approximation
3. Error Estimates for Optimal Values
4. Error estimates for bang-bang solutions
4.1. A lower minorant for minimal values
4.2. Hölder type error estimates
5. Structural stability and improved error estimates
6. Numerical results
Keywords: optimal control; bang-bang control; discretization
Subject classification: Mathematics Subject Classification Code: 49M25 (49J15 49J30 49N10)
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
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 03 Sep 2019 06:13
Last Modified: 03 Sep 2019 06:13
URI: https://eref.uni-bayreuth.de/id/eprint/3715