4,554 research outputs found
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
Consensus Control for Leader-follower Multi-agent Systems under Prescribed Performance Guarantees
This paper addresses the problem of distributed control for leader-follower
multi-agent systems under prescribed performance guarantees. Leader-follower is
meant in the sense that a group of agents with external inputs are selected as
leaders in order to drive the group of followers in a way that the entire
system can achieve consensus within certain prescribed performance transient
bounds. Under the assumption of tree graphs, a distributed control law is
proposed when the decay rate of the performance functions is within a
sufficient bound. Then, two classes of tree graphs that can have additional
followers are investigated. Finally, several simulation examples are given to
illustrate the results.Comment: 8 page
Minimal Actuator Placement with Optimal Control Constraints
We introduce the problem of minimal actuator placement in a linear control
system so that a bound on the minimum control effort for a given state transfer
is satisfied while controllability is ensured. We first show that this is an
NP-hard problem following the recent work of Olshevsky. Next, we prove that
this problem has a supermodular structure. Afterwards, we provide an efficient
algorithm that approximates up to a multiplicative factor of O(logn), where n
is the size of the multi-agent network, any optimal actuator set that meets the
specified energy criterion. Moreover, we show that this is the best
approximation factor one can achieve in polynomial-time for the worst case.
Finally, we test this algorithm over large Erdos-Renyi random networks to
further demonstrate its efficiency.Comment: This version includes all the omitted proofs from the one to appear
in the American Control Conference (ACC) 2015 proceeding
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