7,159 research outputs found
A Semigroup associated to a linear control system on a Lie group
Let us consider a linear control system \Sigma on a connected Lie group G. It
is known that the accessibility set A from the identity e is in general not a
semigroup. In this article we associate a new algebraic object S to \Sigma
which turns out to be a semigroup, allowing the use of the semigroup machinery
to approach \Sigma. In particular, we obtain some controllability results
Invariance Entropy of Hyperbolic Control Sets
In this paper, we improve the known estimates for the invariance entropy of a
nonlinear control system. For sets of complete approximate controllability we
derive an upper bound in terms of Lyapunov exponents and for uniformly
hyperbolic sets we obtain a similar lower bound. Both estimates can be applied
to hyperbolic chain control sets, and we prove that under mild assumptions they
can be merged into a formula
The Hughes model for pedestrian dynamics and congestion modelling
In this paper we present a numerical study of some variations of the Hughes
model for pedestrian flow under different types of congestion effects. The
general model consists of a coupled non-linear PDE system involving an eikonal
equation and a first order conservation law, and it intends to approximate the
flow of a large pedestrian group aiming to reach a target as fast as possible,
while taking into account the congestion of the crowd.
We propose an efficient semi-Lagrangian scheme (SL) to approximate the
solution of the PDE system and we investigate the macroscopic effects of
different penalization functions modelling the congestion phenomena.Comment: 6 page
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