*URN to cite this document:*urn:nbn:de:bvb:703-opus4-12172

## Title data

Pfister, Maximilian:

**Optimal sensor placement for linear systems.**

Bayreuth
,
2013

(
Bachelor thesis,
2013, University of Bayreuth, Faculty of Mathematics, Physics and Computer Sciences)

PDF
Bachelorarbeit_Maximilian_Pfister.pdf - Published Version Available under License Creative Commons BY 3.0: Attribution . Download (807kB) |

## Abstract

The aim of sensor placement is to observe the state of a dynamical system while using only a small part of the available output information. Thus, the observer does not need sensors at every possible node of the system. We use sensor placement because it is not practical for large-scale networks, such as power grids, to place sensors at each node. With an optimal sensor placement we obtain a subset of sensors which minimizes the observer error in comparison to any other subset of the same size. This means we generate an optimal observation with the given number of sensors. We compute the observer error, for the linear dynamical systems we consider, with the H2-norm of the observer error system. In this approach, we optimize both the subset of selected sensors and the observer gain matrix in parallel. The optimization problem is non-convex both in a constraint, which bounds the H2-norm, as well as in the objective function which uses a l0-norm to count the used sensors. To obtain a semidefinite program, we first relax the l0-norm by an iterative reweighted l1-norm. Second, we use a reformulation of the H2-norm with linear matrix inequalities to replace an occuring bilinear and therefore non-convex term. We use this computationally efficient formulation of the sensor placement problem to derive three algorithms. Furthermore, existing algorithms, which do not use the convex reformulation of the optimization problem, were implemented. The algorithms are compared extensively relating to execution time, performance of the chosen sensors, and the applicability on a practical problem. The practical problem is a model of a high-voltage power grid with the aim to measure the phase angles and the frequencies at every node. The result of the comparison is that a algorithm with a greedy approach solves the optimization problem fast and usually with a good solution. However, this algorithm is problematic because the shortsighted greedy approach cannot exclude that a worst case solution is generated. The best results in general were produced by a novel approach made in this thesis. This novel algorithm iteratively solves the relaxed optimization problem and finds near-optimal sensor subsets.

## Further data

Item Type: | Bachelor thesis |
---|---|

Keywords: | Kontrolltheorie; Optimierung; l1-Relaxation; Sensor Placement; Convex Optimization |

DDC Subjects: | 500 Science |

Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties Faculties > Faculty of Mathematics, Physics und Computer Science |

Language: | English |

Originates at UBT: | Yes |

URN: | urn:nbn:de:bvb:703-opus4-12172 |

Date Deposited: | 24 Apr 2014 14:50 |

Last Modified: | 10 May 2017 10:17 |

URI: | https://epub.uni-bayreuth.de/id/eprint/138 |