3 research outputs found
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 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 . 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