# Minimizing Inputs for Strong Structural Controllability

arXiv: https://arxiv.org/abs/1810.07220 · HTML: https://mlsanity.com/paper/1810.07220/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Oct 2018.

## Built on by (most cited first, 1 of 1)

- [Minimize Control Inputs for Strong Structural Controllability Using Reinforcement Learning with Graph Neural Network](https://mlsanity.com/paper/2402.16925/) (2024)

## Abstract (arXiv)

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.