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)


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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 largescale 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 H2norm 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 nonconvex both in a constraint, which bounds the H2norm, as well as in the objective function which uses a l0norm to count the used sensors. To obtain a semidefinite program, we first relax the l0norm by an iterative reweighted l1norm. Second, we use a reformulation of the H2norm with linear matrix inequalities to replace an occuring bilinear and therefore nonconvex 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 highvoltage 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 nearoptimal sensor subsets.
Further data
Item Type:  Bachelor thesis 

Keywords:  Kontrolltheorie; Optimierung; l1Relaxation; 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:703opus412172 
Date Deposited:  24 Apr 2014 14:50 
Last Modified:  10 May 2017 10:17 
URI:  https://epub.unibayreuth.de/id/eprint/138 