2,222 research outputs found
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
On the Projective Geometry of Kalman Filter
Convergence of the Kalman filter is best analyzed by studying the contraction
of the Riccati map in the space of positive definite (covariance) matrices. In
this paper, we explore how this contraction property relates to a more
fundamental non-expansiveness property of filtering maps in the space of
probability distributions endowed with the Hilbert metric. This is viewed as a
preliminary step towards improving the convergence analysis of filtering
algorithms over general graphical models.Comment: 6 page
Optimal Sampling-Based Motion Planning under Differential Constraints: the Driftless Case
Motion planning under differential constraints is a classic problem in
robotics. To date, the state of the art is represented by sampling-based
techniques, with the Rapidly-exploring Random Tree algorithm as a leading
example. Yet, the problem is still open in many aspects, including guarantees
on the quality of the obtained solution. In this paper we provide a thorough
theoretical framework to assess optimality guarantees of sampling-based
algorithms for planning under differential constraints. We exploit this
framework to design and analyze two novel sampling-based algorithms that are
guaranteed to converge, as the number of samples increases, to an optimal
solution (namely, the Differential Probabilistic RoadMap algorithm and the
Differential Fast Marching Tree algorithm). Our focus is on driftless
control-affine dynamical models, which accurately model a large class of
robotic systems. In this paper we use the notion of convergence in probability
(as opposed to convergence almost surely): the extra mathematical flexibility
of this approach yields convergence rate bounds - a first in the field of
optimal sampling-based motion planning under differential constraints.
Numerical experiments corroborating our theoretical results are presented and
discussed
Cluster-based reduced-order modelling of a mixing layer
We propose a novel cluster-based reduced-order modelling (CROM) strategy of
unsteady flows. CROM combines the cluster analysis pioneered in Gunzburger's
group (Burkardt et al. 2006) and and transition matrix models introduced in
fluid dynamics in Eckhardt's group (Schneider et al. 2007). CROM constitutes a
potential alternative to POD models and generalises the Ulam-Galerkin method
classically used in dynamical systems to determine a finite-rank approximation
of the Perron-Frobenius operator. The proposed strategy processes a
time-resolved sequence of flow snapshots in two steps. First, the snapshot data
are clustered into a small number of representative states, called centroids,
in the state space. These centroids partition the state space in complementary
non-overlapping regions (centroidal Voronoi cells). Departing from the standard
algorithm, the probabilities of the clusters are determined, and the states are
sorted by analysis of the transition matrix. Secondly, the transitions between
the states are dynamically modelled using a Markov process. Physical mechanisms
are then distilled by a refined analysis of the Markov process, e.g. using
finite-time Lyapunov exponent and entropic methods. This CROM framework is
applied to the Lorenz attractor (as illustrative example), to velocity fields
of the spatially evolving incompressible mixing layer and the three-dimensional
turbulent wake of a bluff body. For these examples, CROM is shown to identify
non-trivial quasi-attractors and transition processes in an unsupervised
manner. CROM has numerous potential applications for the systematic
identification of physical mechanisms of complex dynamics, for comparison of
flow evolution models, for the identification of precursors to desirable and
undesirable events, and for flow control applications exploiting nonlinear
actuation dynamics.Comment: 48 pages, 30 figures. Revised version with additional material.
Accepted for publication in Journal of Fluid Mechanic
A Survey on Continuous Time Computations
We provide an overview of theories of continuous time computation. These
theories allow us to understand both the hardness of questions related to
continuous time dynamical systems and the computational power of continuous
time analog models. We survey the existing models, summarizing results, and
point to relevant references in the literature
Estimation and control of non-linear and hybrid systems with applications to air-to-air guidance
Issued as Progress report, and Final report, Project no. E-21-67
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