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The notion of strong structural controllability (s-controllability) allowsfor determining controllability properties of large linear time-invariantsystems even when numerical values of the system parameters are not known apriori. The s-controllability guarantees controllability for all numericalrealizations of the system parameters. We address the optimization problem ofminimal cardinality input selection for s-controllability. Previous work showsthat not only the optimization problem is NP-hard, but finding an approximatesolution is also hard. We propose a randomized algorithm using the notion ofzero forcing sets to obtain an optimal solution with high probability. Wecompare the performance of the proposed algorithm with a known heuristic [1]for synthetic random systems and five real-world networks, viz. IEEE 39-bussystem, re-tweet network, protein-protein interaction network, US airportnetwork, and a network of physicians. It is found that our algorithm performsmuch better than the heuristic in each of these cases.

Minimizing Inputs for Strong Structural Controllability