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arXiv · 2007.07541

Prototypical Description and Controller Design for a Set of Systems Using v-gap Based Clustering

Lukas Munser·Arne-Jens Hempel·Grigory Devadze·Stefan Streif
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Abstract

We present an approach to design stabilizing controllers for a set of linear systems without restrictions regarding their modeling order. To this end, the systems are treated as abstract objects in the space of the $ν$-gap metric. Via a cluster analysis the set of systems is split into v-gap similar clusters which are treated separately. For this purpose we provide an algorithm that constructs an explicit prototype system by generalizing the information of a given set of systems. Applying this algorithm to each cluster a set of prototype systems is obtained. Given these prototypes we design controllers in such a way that all systems assigned to a cluster will be stabilized by a corresponding controller. The approach is demonstrated for a set of 80 linear systems.

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Lukas Munser, Arne-Jens Hempel, Grigory Devadze, Stefan Streif. 2020-07-15. Prototypical Description and Controller Design for a Set of Systems Using v-gap Based Clustering. https://arxiv.org/abs/2007.07541

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