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

TL;DR

This paper introduces a method to design stabilizing controllers for multiple linear systems by clustering them based on the v-gap metric and creating prototype systems for each cluster, enabling efficient control design.

Contribution

The paper proposes a novel clustering-based approach using v-gap metric to construct prototype systems for stabilizing controller design across diverse linear systems.

Findings

Successfully applied to 80 linear systems

Clusters systems with similar control characteristics

Achieved stable control for all systems in the set

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 $\nu$-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.