Minimal Structural Perturbations for Network Controllability: Complexity
Analysis
release_nsbyce4zn5ex5mmyt4y6yfnj2a
by
Yuan Zhang, Tong Zhou
2018
Abstract
Link (edge) addition/deletion or sensor/actuator failures are common
structural perturbations for real network systems. This paper is related to the
computation complexity of minimal (cost) link insertion, deletion and vertex
deletion with respect to structural controllability of networks. Formally,
given a structured system, we prove that: i) it is NP-hard to add the minimal
cost of links (including links between state variables and from inputs to state
variables) from a given set of links to make the system structurally
controllable, even with identical link costs or a prescribed input topology;
ii) it is NP-hard to determine the minimal cost of links whose deletion
deteriorates structural controllability of the system, even with identical link
costs or when the removable links are restricted in input links. It is also
proven that determining the minimal cost of inputs whose deletion causes
structural uncontrollability is NP-hard in the strong sense. The reductions in
their proofs are technically independent. These results may serve an answer to
the general hardness of optimally designing (modifying) a structurally
controllable network topology and of measuring controllability robustness
against link/actuator failures. Some fundamental approximation results for
these related problems are also provided.
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