## Title data

Baier, Robert ; Büskens, Christof ; Chahma, Ilyes Aïssa ; Gerdts, Matthias:

**Approximation of reachable sets by direct solution methods for optimal control problems.**

*In:* Optimization Methods and Software.
Vol. 22
(2007)
Issue 3
.
- pp. 433-452.

ISSN 1029-4937

DOI: https://doi.org/10.1080/10556780600604999

Review: |

## Abstract in another language

A numerical method for the approximation of reachable sets of linear control systems is discussed. The method is based on the formulation of suitable optimal control problems with varying objective function, whose discretization by Runge-Kutta methods leads to finite-dimensional convex optimization problems. It turns out that the order of approximation for the reachable set depends on the particular choice of the Runge-Kutta method in combination with the selection strategy used for control approximation. For an inappropriate combination, the expected order of convergence cannot be achieved in general. The method is illustrated by two test examples using different Runge-Kutta methods and selection strategies, in which the run times are analysed, the order of convergence is estimated numerically and compared with theoretical results in similar areas.

## Further data

Item Type: | Article in a journal |
---|---|

Refereed: | Yes |

Additional notes: | Contents:
1. Introduction 2. Notation 3. Direct solution method for the approximation of reachable sets 3.1 Connection to OCPs 3.2 Approximation of reachable sets by discretized OCPs 3.3 Discrete reachable sets 3.4 Implementation 4. Examples 5. Outline of further research |

Keywords: | Approximation of reachable sets; Discretization of optimal control problems; Direct solution methods; Set-valued Runge-Kutta methods; Order of convergence; Linear optimal control problems |

Subject classification: | Mathematics Subject Classification Code: 93B03 (65L06 49J53 49N05 49M25 93B40) |

Institutions of the University: | 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) |

Result of work at the UBT: | Yes |

DDC Subjects: | 500 Science 500 Science > 510 Mathematics |

Date Deposited: | 03 Mar 2021 10:52 |

Last Modified: | 25 Mar 2021 06:03 |

URI: | https://eref.uni-bayreuth.de/id/eprint/63622 |