1,802 research outputs found
On the reachability and observability of path and cycle graphs
In this paper we investigate the reachability and observability properties of
a network system, running a Laplacian based average consensus algorithm, when
the communication graph is a path or a cycle. More in detail, we provide
necessary and sufficient conditions, based on simple algebraic rules from
number theory, to characterize all and only the nodes from which the network
system is reachable (respectively observable). Interesting immediate
corollaries of our results are: (i) a path graph is reachable (observable) from
any single node if and only if the number of nodes of the graph is a power of
two, , and (ii) a cycle is reachable (observable) from
any pair of nodes if and only if is a prime number. For any set of control
(observation) nodes, we provide a closed form expression for the (unreachable)
unobservable eigenvalues and for the eigenvectors of the (unreachable)
unobservable subsystem
A Tight Lower Bound on the Controllability of Networks with Multiple Leaders
In this paper we study the controllability of networked systems with static
network topologies using tools from algebraic graph theory. Each agent in the
network acts in a decentralized fashion by updating its state in accordance
with a nearest-neighbor averaging rule, known as the consensus dynamics. In
order to control the system, external control inputs are injected into the so
called leader nodes, and the influence is propagated throughout the network.
Our main result is a tight topological lower bound on the rank of the
controllability matrix for such systems with arbitrary network topologies and
possibly multiple leaders
Leader-following Consensus of Multi-agent Systems over Finite Fields
The leader-following consensus problem of multi-agent systems over finite
fields is considered in this paper. Dynamics of each agent is
governed by a linear equation over , where a distributed control
protocol is utilized by the followers.Sufficient and/or necessary conditions on
system matrices and graph weights in are provided for the
followers to track the leader
Controllability and Fraction of Leaders in Infinite Network
In this paper, we study controllability of a network of linear
single-integrator agents when the network size goes to infinity. We first
investigate the effect of increasing size by injecting an input at every node
and requiring that network controllability Gramian remain well-conditioned with
the increasing dimension. We provide theoretical justification to the intuition
that high degree nodes pose a challenge to network controllability. In
particular, the controllability Gramian for the networks with bounded maximum
degrees is shown to remain well-conditioned even as the network size goes to
infinity. In the canonical cases of star, chain and ring networks, we also
provide closed-form expressions which bound the condition number of the
controllability Gramian in terms of the network size. We next consider the
effect of the choice and number of leader nodes by actuating only a subset of
nodes and considering the least eigenvalue of the Gramian as the network size
increases. Accordingly, while a directed star topology can never be made
controllable for all sizes by injecting an input just at a fraction of
nodes; for path or cycle networks, the designer can actuate a non-zero fraction
of nodes and spread them throughout the network in such way that the least
eigenvalue of the Gramians remain bounded away from zero with the increasing
size. The results offer interesting insights on the challenges of control in
large networks and with high-degree nodes.Comment: 6 pages, 3 figures, to appear in 2014 IEEE CD
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