6 research outputs found
Binary interaction algorithms for the simulation of flocking and swarming dynamics
Microscopic models of flocking and swarming takes in account large numbers of
interacting individ- uals. Numerical resolution of large flocks implies huge
computational costs. Typically for interacting individuals we have a cost
of . We tackle the problem numerically by considering approximated
binary interaction dynamics described by kinetic equations and simulating such
equations by suitable stochastic methods. This approach permits to compute
approximate solutions as functions of a small scaling parameter
at a reduced complexity of O(N) operations. Several numerical results show the
efficiency of the algorithms proposed
Sparse Control of Alignment Models in High Dimension
For high dimensional particle systems, governed by smooth nonlinearities
depending on mutual distances between particles, one can construct
low-dimensional representations of the dynamical system, which allow the
learning of nearly optimal control strategies in high dimension with
overwhelming confidence. In this paper we present an instance of this general
statement tailored to the sparse control of models of consensus emergence in
high dimension, projected to lower dimensions by means of random linear maps.
We show that one can steer, nearly optimally and with high probability, a
high-dimensional alignment model to consensus by acting at each switching time
on one agent of the system only, with a control rule chosen essentially
exclusively according to information gathered from a randomly drawn
low-dimensional representation of the control system.Comment: 39 page