Clustering Techniques for Stable Linear Dynamical Systems with applications to Hard Disk Drives

Abstract: In Robust Control and Data Driven Robust Control design methodologies, multiple plant transfer functions or a family of transfer functions are considered and a common controller is designed such that all the plants that fall into this family are stabilized. Though the plants are stabilized, the controller might be sub-optimal for each of the plants when the variations in the plants are large. This paper presents a way of clustering stable linear dynamical systems for the design of robust controllers within each of the clusters such that the controllers are optimal for each of the clusters. First a k-medoids algorithm for hard clustering will be presented for stable Linear Time Invariant (LTI) systems and then a Gaussian Mixture Models (GMM) clustering for a special class of LTI systems, common for Hard Disk Drive plants, will be presented. Keywords: Robust Control, Clustering, k-medoids, Gaussian Mixture Models, Hard Disk Drives 1. INTRODUCTION Recently, in most of the personal computers, Solid State Drives (SSD) have replaced HDDs as the data transfer rate of SSDs is much higher than that of HDDs.