Performance bounds for optimal feedback control in networks

TL;DR

This paper investigates the fundamental limits of feedback control performance in complex networks, highlighting how network structure and dynamics influence control costs and actuator effectiveness.

Contribution

It provides novel bounds on control costs based on network dynamics and actuator placement, including tradeoffs and worst-case performance analysis.

Findings

Optimal control cost can grow exponentially with network size for unstable systems.

Performance bounds depend on system dynamics and actuator configuration.

Numerical experiments demonstrate bounds on regular and random networks.

Abstract

Many important complex networks, including critical infrastructure and emerging industrial automation systems, are becoming increasingly intricate webs of interacting feedback control loops. A fundamental concern is to quantify the control properties and performance limitations of the network as a function of its dynamical structure and control architecture. We study performance bounds for networks in terms of optimal feedback control costs. We provide a set of complementary bounds as a function of the system dynamics and actuator structure. For unstable network dynamics, we characterize a tradeoff between feedback control performance and the number of control inputs, in particular showing that optimal cost can increase exponentially with the size of the network. We also derive a bound on the performance of the worst-case actuator subset for stable networks, providing insight into dynamics properties that affect the potential efficacy of actuator selection. We illustrate our results with numerical experiments that analyze performance in regular and random networks.