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

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

A parameterization of observer-based controllers: Bumpless transfer by covariance interpolation

Abstract — This paper presents an algorithm to interpolate between two observer-based controllers for a linear multivari-able system such that the closed loop system remains stable throughout the interpolation. The method interpolates between the inverse Lyapunov functions for the two original state feedbacks and between the Lyapunov functions for the two original observer gains to determine an intermediate observer-based controller. I

Schematics of metric (top) vs. topological (bottom) neighborhood of interactions.

<p> is the radius of the metric neighborhood and <i>r</i> is the radius of the topological one based on the rule of <i>k</i>-nearest neighbors with . <i>R</i> is constant as it defines a metric zone around the agent while <i>r</i> changes in accordance with the distance between the agent and its <i>k</i>-th (here 7-th) nearest neighbor.</p

Alignment versus noise level for a swarm comprised of agents.

<p>Three values of the outdegree are considered: and 10.</p

Critical value of the number of topological neighbors, , for which the connectedness of the network is guaranteed, as a function of the swarm size , with ranging from 10 to 1000.

<p>Grey dots represent the average value of obtained from a statistical analysis comprising 1000 randomly generated <i>k</i>-nearest digraphs. The errorbars represent the associated standard deviations.</p