## Title data

Grüne, Lars ; Junge, Oliver:

**Constructing Robust Feedback Laws by Set Oriented Numerical Methods.**

*In:* Proceedings in Applied Mathematics and Mechanics.
Vol. 5
(December 2005)
Issue 1
.
- pp. 157-160.

ISSN 1617-7061

DOI: https://doi.org/10.1002/pamm.200510059

## Abstract in another language

In two previous papers [Junge, Osinga 04; Grüne, Junge 05] a numerical method for the construction of optimally stabilizing feedback laws was proposed. The method is based on a set oriented discretization of phase space in combination with graph theoretic algorithms for the computation of shortest paths in directed weighted graphs. The resulting approximate optimal value function is piecewise constant, yielding an approximate optimal feedback which might not be robust with respect to perturbations of the system. In this contribution we extend the approach to the case of perturbed control systems. Based on the concept of a multivalued game we show how to derive a directed weighted hypergraph from the original system and generalize the corresponding shortest path algorithm. The resulting optimal value function yields a robustly stabilizing approximate optimal feedback law. This note is an abbreviated version of [Grüne, Junge 05a]. For the proofs of the statements here we refer to the full paper.

## Further data

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

Refereed: | Yes |

Additional notes: | Special Issue: GAMM Annual Meeting 2005 - Luxembourg |

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) 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 |

Result of work at the UBT: | Yes |

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

Date Deposited: | 02 Mar 2021 10:26 |

Last Modified: | 23 Mar 2021 09:13 |

URI: | https://eref.uni-bayreuth.de/id/eprint/63561 |