## 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: |

## Related URLs

## 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: | linear-quadratic 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 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 |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science > 510 Mathematics |

Date Deposited: | 03 Sep 2019 06:13 |

Last Modified: | 28 May 2021 09:49 |

URI: | https://eref.uni-bayreuth.de/id/eprint/3715 |