Distributed Design of Glocal Controllers via Hierarchical Model Decomposition

This article proposes a distributed design method of controllers with a glocal (global/local) information structure for large-scale network systems. The glocal controller of interest has a hierarchical structure, wherein a global subcontroller coordinates a set of disjoint local subcontrollers. The global subcontroller regulates interarea oscillations among subsystems, while local subcontrollers individually regulate intraarea oscillations of the respective subsystem. The distributed design of the glocal controller is addressed to enhance the scalability of controller synthesis, where the global subcontroller and all local subcontrollers are designed independently of each other. A design problem is formulated for subcontroller sets such that any combination of subcontrollers each of which belongs to its corresponding set guarantees stability of the closed-loop system. The core idea of the proposed method is to represent the original network system as a hierarchical cascaded system composed of reduced-order models representing the interarea and intraarea dynamics, referred to as hierarchical model decomposition. Distributed design is achieved by virtue of the cascade structure. The primary findings of this study are twofold. First, a tractable solution to the distributed design problem and an existence condition of the hierarchical model decomposition are presented. Second, a clustering method appropriate for the proposed framework and a robust extension are provided. Numerical examples of a power grid highlight the practical relevance of the proposed method.