7,136 research outputs found
Wardrop Equilibrium in Discrete-Time Selfish Routing with Time-Varying Bounded Delays
This paper presents a multi-commodity, discrete-
time, distributed and non-cooperative routing algorithm, which is
proved to converge to an equilibrium in the presence of
heterogeneous, unknown, time-varying but bounded delays.
Under mild assumptions on the latency functions which describe
the cost associated to the network paths, two algorithms are
proposed: the former assumes that each commodity relies only on
measurements of the latencies associated to its own paths; the
latter assumes that each commodity has (at least indirectly) access
to the measures of the latencies of all the network paths. Both
algorithms are proven to drive the system state to an invariant set
which approximates and contains the Wardrop equilibrium,
defined as a network state in which no traffic flow over the
network paths can improve its routing unilaterally, with the latter
achieving a better reconstruction of the Wardrop equilibrium.
Numerical simulations show the effectiveness of the proposed
approach
A detectability criterion and data assimilation for non-linear differential equations
In this paper we propose a new sequential data assimilation method for
non-linear ordinary differential equations with compact state space. The method
is designed so that the Lyapunov exponents of the corresponding estimation
error dynamics are negative, i.e. the estimation error decays exponentially
fast. The latter is shown to be the case for generic regular flow maps if and
only if the observation matrix H satisfies detectability conditions: the rank
of H must be at least as great as the number of nonnegative Lyapunov exponents
of the underlying attractor. Numerical experiments illustrate the exponential
convergence of the method and the sharpness of the theory for the case of
Lorenz96 and Burgers equations with incomplete and noisy observations
Complex Dynamics and Synchronization of Delayed-Feedback Nonlinear Oscillators
We describe a flexible and modular delayed-feedback nonlinear oscillator that
is capable of generating a wide range of dynamical behaviours, from periodic
oscillations to high-dimensional chaos. The oscillator uses electrooptic
modulation and fibre-optic transmission, with feedback and filtering
implemented through real-time digital-signal processing. We consider two such
oscillators that are coupled to one another, and we identify the conditions
under which they will synchronize. By examining the rates of divergence or
convergence between two coupled oscillators, we quantify the maximum Lyapunov
exponents or transverse Lyapunov exponents of the system, and we present an
experimental method to determine these rates that does not require a
mathematical model of the system. Finally, we demonstrate a new adaptive
control method that keeps two oscillators synchronized even when the coupling
between them is changing unpredictably.Comment: 24 pages, 13 figures. To appear in Phil. Trans. R. Soc. A (special
theme issue to accompany 2009 International Workshop on Delayed Complex
Systems
Mathematical control of complex systems
Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
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