14,575 research outputs found
Structural Target Controllability of Undirected Networks
In this paper, we study the target controllability problem of networked
dynamical systems, in which we are tasked to steer a subset of network states
towards a desired objective. More specifically, we derive necessary and
sufficient conditions for the structural target controllability problem of
linear time-invariant (LTI) systems with symmetric state matrices, such as
undirected dynamical networks with unknown link weights. To achieve our goal,
we first characterize the generic rank of symmetrically structured matrices, as
well as the modes of any numerical realization. Subsequently, we provide a
graph-theoretic necessary and sufficient condition for the structural
controllability of undirected networks with multiple control nodes. Finally, we
derive a graph-theoretic necessary and sufficient condition for structural
target controllability of undirected networks. Remarkably, apart from the
standard reachability condition, only local topological information is needed
for the verification of structural target controllability
Controllability Metrics, Limitations and Algorithms for Complex Networks
This paper studies the problem of controlling complex networks, that is, the
joint problem of selecting a set of control nodes and of designing a control
input to steer a network to a target state. For this problem (i) we propose a
metric to quantify the difficulty of the control problem as a function of the
required control energy, (ii) we derive bounds based on the system dynamics
(network topology and weights) to characterize the tradeoff between the control
energy and the number of control nodes, and (iii) we propose an open-loop
control strategy with performance guarantees. In our strategy we select control
nodes by relying on network partitioning, and we design the control input by
leveraging optimal and distributed control techniques. Our findings show
several control limitations and properties. For instance, for Schur stable and
symmetric networks: (i) if the number of control nodes is constant, then the
control energy increases exponentially with the number of network nodes, (ii)
if the number of control nodes is a fixed fraction of the network nodes, then
certain networks can be controlled with constant energy independently of the
network dimension, and (iii) clustered networks may be easier to control
because, for sufficiently many control nodes, the control energy depends only
on the controllability properties of the clusters and on their coupling
strength. We validate our results with examples from power networks, social
networks, and epidemics spreading
Controllability of structural brain networks.
Cognitive function is driven by dynamic interactions between large-scale neural circuits or networks, enabling behaviour. However, fundamental principles constraining these dynamic network processes have remained elusive. Here we use tools from control and network theories to offer a mechanistic explanation for how the brain moves between cognitive states drawn from the network organization of white matter microstructure. Our results suggest that densely connected areas, particularly in the default mode system, facilitate the movement of the brain to many easily reachable states. Weakly connected areas, particularly in cognitive control systems, facilitate the movement of the brain to difficult-to-reach states. Areas located on the boundary between network communities, particularly in attentional control systems, facilitate the integration or segregation of diverse cognitive systems. Our results suggest that structural network differences between cognitive circuits dictate their distinct roles in controlling trajectories of brain network function
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