Scalable distributed and decentralized $\mathscr{H}_2$ controller synthesis for interconnected linear discrete-time systems
Abstract
The current limitation in the synthesis of distributed controllers for linear interconnected systems is scalability due to non-convex or unstructured synthesis conditions. In this paper we develop convex and structured conditions for the existence of a distributed controller for discrete-time interconnected systems with an interconnection structure that corresponds to an arbitrary graph. Neutral interconnections and a storage function with a block-diagonal structure are utilized to attain coupling conditions that are of a considerably lower computational complexity compared to the corresponding centralized controller synthesis problem. Additionally, the developed conditions are adapted for the corresponding decentralized controller synthesis problem with fixed supply functions for the interconnections. The effectiveness and scalability of the developed distributed controller synthesis method is demonstrated for small- to large-scale oscillator networks on a cycle graph.
Cite
@article{arxiv.2001.04875,
title = {Scalable distributed and decentralized $\mathscr{H}_2$ controller synthesis for interconnected linear discrete-time systems},
author = {Tom R. V. Steentjes and Mircea Lazar and Paul M. J. Van den Hof},
journal= {arXiv preprint arXiv:2001.04875},
year = {2021}
}
Comments
Changes in this version include: overview of dissipativity-based results for interconnected systems is removed, result on the existence of a decentralized controller is included and a simulation example for the illustration of scalability replaces the previous simulation example