*URN to cite this document:*urn:nbn:de:bvb:703-epub-3577-0

## Title data

Yegorov, Ivan ; Dower, Peter ; Grüne, Lars:

**A characteristics based curse-of-dimensionality-free approach for approximating control Lyapunov functions and feedback stabilization.**

Bayreuth ; Melbourne
,
2018
. - 8 S.

## Project information

Project title: |
Project's official title Project's id Activating Lyapunov-Based Feedback - Nonsmooth Control Lyapunov Functions DP160102138 No information FA2386-16-1-4066 |
---|---|

Project financing: |
ARC (Australian Research Council) AFOSR/AOARD |

## Abstract

This paper develops a curse-of-dimensionality-free numerical approach to construct control Lyapunov functions (CLFs) and stabilizing feedback strategies for deterministic con- trol systems described by systems of ODEs. An extension of the Zubov method is used to represent a CLF as the value function for an appropriate infinite-horizon optimal control problem. The infinite-horizon stabilization problem is approximated by an exit time problem, with target set given by a sufficiently small closed neighborhood of the origin in the state space. In order to compute the related value function and optimal feedback control law separately at different initial states and thereby to attenuate the curse of dimensionality, an extension of a recently developed characteristics based framework is proposed. Theoretical foundations of the developed approach are given together with practical discussions regarding its implementation, and numerical examples are also provided. In particular, it is pointed out that the curse of complexity may remain a significant issue even if the curse of dimensionality is avoided.

## Further data

Item Type: | Preprint, postprint |
---|---|

Additional notes (visible to public): | erschienen in:
Proceedings of the 23rd International Symposium on Mathematical Theory of Networks and Systems. - Hong Kong , 2018 . - S. 342-349 |

Keywords: | control Lyapunov functions; optimal control; optimization; stabilization by feedback |

DDC Subjects: | 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 Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics 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-3577-0 |

Date Deposited: | 12 Feb 2018 07:40 |

Last Modified: | 14 May 2021 08:53 |

URI: | https://epub.uni-bayreuth.de/id/eprint/3577 |