Minimizing Inputs for Strong Structural Controllability

TL;DR

This paper introduces a randomized algorithm leveraging zero forcing sets to efficiently find minimal input sets ensuring strong structural controllability in large systems, outperforming existing heuristics.

Contribution

It presents a novel randomized approach for minimal input selection in s-controllability, addressing NP-hardness and demonstrating superior performance over heuristics.

Findings

Algorithm achieves high-probability optimal solutions

Performs better than existing heuristics on various networks

Effective on both synthetic and real-world systems

Abstract

The notion of strong structural controllability (s-controllability) allows for determining controllability properties of large linear time-invariant systems even when numerical values of the system parameters are not known a priori. The s-controllability guarantees controllability for all numerical realizations of the system parameters. We address the optimization problem of minimal cardinality input selection for s-controllability. Previous work shows that not only the optimization problem is NP-hard, but finding an approximate solution is also hard. We propose a randomized algorithm using the notion of zero forcing sets to obtain an optimal solution with high probability. We compare the performance of the proposed algorithm with a known heuristic [1] for synthetic random systems and five real-world networks, viz. IEEE 39-bus system, re-tweet network, protein-protein interaction network, US airport network, and a network of physicians. It is found that our algorithm performs much better than the heuristic in each of these cases.