A Graphical Characterization of Structurally Controllable Linear Systems with Dependent Parameters

One version of the concept of structural controllability defined for single-input systems by Lin and subsequently generalized to multi-input systems by others, states that a parameterized matrix pair $(A, B)$ whose nonzero entries are distinct parameters, is structurally controllable if values can be assigned to the parameters which cause the resulting matrix pair to be controllable. In this paper the concept of structural controllability is broadened to allow for the possibility that a parameter may appear in more than one location in the pair $(A, B)$. Subject to a certain condition on the parameterization called the "binary assumption", an explicit graph-theoretic characterization of such matrix pairs is derived

Minimal Structural Perturbations for Network Controllability: Complexity Analysis

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.Comment: Revised structure. This work is an extension of the CDC conference paper. International Journal of Robust and Nonlinear Control (2019

Structural Controllability of a Networked Dynamic System with LFT Parameterized Subsystems

This paper studies structural controllability for a networked dynamic system (NDS), in which each subsystem may have different dynamics, and unknown parameters may exist both in subsystem dynamics and in subsystem interconnections. In addition, subsystem parameters are parameterized by a linear fractional transformation (LFT). It is proven that controllability keeps to be a generic property for this kind of NDSs. Some necessary and sufficient conditions are then established respectively for them to be structurally controllable, to have a fixed uncontrollable mode, and to have a parameter dependent uncontrollable mode, under the condition that each subsystem interconnection link can take a weight independently. These conditions are scalable, and in their verifications, all arithmetic calculations are performed separately on each subsystem. In addition, these conditions also reveal influences on NDS controllability from subsystem input-output relations, subsystem uncontrollable modes and subsystem interconnection topology. Based on these observations, the problem of selecting the minimal number of subsystem interconnection links is studied under the requirement of constructing a structurally controllable NDS. A heuristic method is derived with some provable approximation bounds and a low computational complexity.Comment: Accepted by IEEE Transactions on Automatic Control as full paper, scheduled to appear in Volume 64 (2019), Issue 12 (December