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This paper studies the problem of modifying the input matrix of a structuredsystem to make the system strongly structurally controllable. We focus on thegeneralized structured systems that rely on zero/nonzero/arbitrary structure,i.e., some entries of system matrices are zeros, some are nonzero, and theremaining entries can be zero or nonzero (arbitrary). We analyze thefeasibility of the problem, and if it is feasible, we reformulate it intoanother equivalent problem. This new formulation leads to a greedy heuristicalgorithm. However, we also show that the greedy algorithm can give arbitrarilypoor solutions for some special systems. Our alternative approach is arandomized Markov chain Monte Carlo-based algorithm. Unlike the greedyalgorithm, this algorithm is guaranteed to converge to an optimal solution withhigh probability. Finally, we numerically evaluate the algorithms on randomgraphs to show that the algorithms perform well.

Minimal Input Structural Modifications for Strongly Structural Controllability