Actuator Placement for Structural Controllability beyond Strong Connectivity and towards Robustness

TL;DR

This paper develops improved algorithms for actuator placement in large-scale networks to ensure structural controllability and robustness, even with actuator failures, extending classical methods to more general graph structures.

Contribution

It introduces an extended greedy algorithm for actuator placement on non-strongly connected graphs and analyzes minimal backup placements for robustness.

Findings

Extended greedy algorithm outperforms classical methods.

Proved the backup placement problem is NP-hard.

Validated results through numerical case study.

Abstract

Actuator placement is a fundamental problem in control design for large-scale networks. In this paper, we study the problem of finding a set of actuator positions by minimizing a given metric, while satisfying a structural controllability requirement and a constraint on the number of actuators. We first extend the classical forward greedy algorithm for applications to graphs that are not necessarily strongly connected. We then improve this greedy algorithm by extending its horizon. This is done by evaluating the actuator position set expansions at the further steps of the classical greedy algorithm. We prove that this new method attains a better performance, when this evaluation considers the final actuator position set. Moreover, we study the problem of minimal backup placements. The goal is to ensure that the system stays structurally controllable even when any of the selected actuators goes offline, with minimum number of backup actuators. We show that this problem is equivalent to the well-studied NP-hard hitting set problem. Our results are verified by a numerical case study.