Distributed Optimization for Control

TLDR

Advances in wired and wireless technology have driven the need for theory, models, and tools that address large‑scale control and optimization over networks, where classical centralized optimization fails because each node only has local information and a local view of the network. This review surveys the development of distributed computational models for time‑varying networks. The authors focus on a simple direct primal (sub)gradient method to highlight network structure effects, while also reviewing other distributed optimization methods for networks. The review presents applications of the distributed optimization framework to power‑system control, least‑squares solutions of linear equations, and model‑predictive control.

Abstract

Advances in wired and wireless technology have necessitated the development of theory, models, and tools to cope with the new challenges posed by large-scale control and optimization problems over networks. The classical optimization methodology works under the premise that all problem data are available to a central entity (a computing agent or node). However, this premise does not apply to large networked systems, where each agent (node) in the network typically has access only to its private local information and has only a local view of the network structure. This review surveys the development of such distributed computational models for time-varying networks. To emphasize the role of the network structure in these approaches, we focus on a simple direct primal (sub)gradient method, but we also provide an overview of other distributed methods for optimization in networks. Applications of the distributed optimization framework to the control of power systems, least squares solutions to linear equations, and model predictive control are also presented.