15 research outputs found
Controllability of a swarm of topologically interacting autonomous agents
Controllability of complex networks has been the focal point of many recent
studies in the field of complexity. These landmark advances shed a new light on
the dynamics of natural and technological complex systems. Here, we analyze the
controllability of a swarm of autonomous self-propelled agents having a
topological neighborhood of interactions, applying the analytical tools
developed for the study of the controllability of arbitrary complex directed
networks. To this aim we thoroughly investigate the structural properties of
the swarm signaling network which is the information transfer channel
underpinning the dynamics of agents in the physical space. Our results show
that with 6 or 7 topological neighbors, every agent not only affects, but is
also affected by all other agents within the group. More importantly, still
with 6 or 7 topological neighbors, each agent is capable of full control over
all other agents. This finding is yet another argument justifying the
particular value of the number of topological neighbors observed in field
observations with flocks of starlings.Comment: 9 pages, 3 figures. arXiv admin note: text overlap with
arXiv:1401.259
Minimum Number of Probes for Brain Dynamics Observability
In this paper, we address the problem of placing sensor probes in the brain
such that the system dynamics' are generically observable. The system dynamics
whose states can encode for instance the fire-rating of the neurons or their
ensemble following a neural-topological (structural) approach, and the sensors
are assumed to be dedicated, i.e., can only measure a state at each time. Even
though the mathematical description of brain dynamics is (yet) to be
discovered, we build on its observed fractal characteristics and assume that
the model of the brain activity satisfies fractional-order dynamics.
Although the sensor placement explored in this paper is particularly
considering the observability of brain dynamics, the proposed methodology
applies to any fractional-order linear system. Thus, the main contribution of
this paper is to show how to place the minimum number of dedicated sensors,
i.e., sensors measuring only a state variable, to ensure generic observability
in discrete-time fractional-order systems for a specified finite interval of
time. Finally, an illustrative example of the main results is provided using
electroencephalogram (EEG) data.Comment: arXiv admin note: text overlap with arXiv:1507.0720
Resilience and Controllability of Dynamic Collective Behaviors
The network paradigm is used to gain insight into the structural root causes
of the resilience of consensus in dynamic collective behaviors, and to analyze
the controllability of the swarm dynamics. Here we devise the dynamic signaling
network which is the information transfer channel underpinning the swarm
dynamics of the directed interagent connectivity based on a topological
neighborhood of interactions. The study of the connectedness of the swarm
signaling network reveals the profound relationship between group size and
number of interacting neighbors, which is found to be in good agreement with
field observations on flock of starlings [Ballerini et al. (2008) Proc. Natl.
Acad. Sci. USA, 105: 1232]. Using a dynamical model, we generate dynamic
collective behaviors enabling us to uncover that the swarm signaling network is
a homogeneous clustered small-world network, thus facilitating emergent
outcomes if connectedness is maintained. Resilience of the emergent consensus
is tested by introducing exogenous environmental noise, which ultimately
stresses how deeply intertwined are the swarm dynamics in the physical and
network spaces. The availability of the signaling network allows us to
analytically establish for the first time the number of driver agents necessary
to fully control the swarm dynamics
Graph Theoretic Analysis of Multi-Agent system Structural Properties
Ph.DDOCTOR OF PHILOSOPH
Structural Controllability of Discrete-Time Linear Control Systems with Time-Delay: A Delay Node Inserting Approach
This paper is concerned with the structural controllability analysis for discrete-time linear control systems with time-delay. By adding virtual delay nodes, the linear systems with time-delay are transformed into corresponding linear systems without time-delay, and the structural controllability of them is equivalent. That is to say, the time-delay does not affect or change the controllability of the systems. Several examples are also presented to illustrate the theoretical results