Clustering Techniques for Stable Linear Dynamical Systems with applications to Hard Disk Drives
This work addresses controller optimization for robust control in systems like Hard Disk Drives, but it appears incremental as it applies existing clustering methods to a known bottleneck.
This paper tackles the problem of sub-optimal robust controllers for stable linear dynamical systems with large variations by clustering the systems to design optimal controllers within each cluster, presenting k-medoids for general LTI systems and Gaussian Mixture Models for a specific class relevant to Hard Disk Drives.
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.