8,760 research outputs found
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
Multirhythmicity in an optoelectronic oscillator with large delay
An optoelectronic oscillator exhibiting a large delay in its feedback loop is
studied both experimentally and theoretically. We show that multiple
square-wave oscillations may coexist for the same values of the parameters
(multirhythmicity). Depending on the sign of the phase shift, these regimes
admit either periods close to an integer fraction of the delay or periods close
to an odd integer fraction of twice the delay. These periodic solutions emerge
from successive Hopf bifurcation points and stabilize at a finite amplitude
following a scenario similar to Eckhaus instability in spatially extended
systems. We find quantitative agreements between experiments and numerical
simulations. The linear stability of the square-waves is substantiated
analytically by determining stable fixed points of a map.Comment: 14 pages, 7 figure
Tracking azimuthons in nonlocal nonlinear media
We study the formation of azimuthons, i.e., rotating spatial solitons, in
media with nonlocal focusing nonlinearity. We show that whole families of these
solutions can be found by considering internal modes of classical non-rotating
stationary solutions, namely vortex solitons. This offers an exhaustive method
to identify azimuthons in a given nonlocal medium. We demonstrate formation of
azimuthons of different vorticities and explain their properties by considering
the strongly nonlocal limit of accessible solitons.Comment: 11 pages, 7 figure
Adaptive Control By Regulation-Triggered Batch Least-Squares Estimation of Non-Observable Parameters
The paper extends a recently proposed indirect, certainty-equivalence,
event-triggered adaptive control scheme to the case of non-observable
parameters. The extension is achieved by using a novel Batch Least-Squares
Identifier (BaLSI), which is activated at the times of the events. The BaLSI
guarantees the finite-time asymptotic constancy of the parameter estimates and
the fact that the trajectories of the closed-loop system follow the
trajectories of the nominal closed-loop system ("nominal" in the sense of the
asymptotic parameter estimate, not in the sense of the true unknown parameter).
Thus, if the nominal feedback guarantees global asymptotic stability and local
exponential stability, then unlike conventional adaptive control, the newly
proposed event-triggered adaptive scheme guarantees global asymptotic
regulation with a uniform exponential convergence rate. The developed adaptive
scheme is tested to a well-known control problem: the state regulation of the
wing-rock model. Comparisons with other adaptive schemes are provided for this
particular problem.Comment: 29 pages, 12 figure
Nonlinear Rescaling of Control Laws with Application to Stabilization in the Presence of Magnitude Saturation
Motivated by some recent results on the stabilization of homogeneous systems, we present a gain-scheduling approach for the stabilization of non-linear systems. Given
a one-parameter family of stabilizing feedbacks and associated Lyapunov functions, we show how the parameter can be rescaled as a function of the state to give a new
stabilizing controller. In the case of homogeneous systems, we obtain generalizations of some existing results. We show that this approach can also be applied to nonhomogeneous
systems. In particular, the main application considered in this paper is to the problem of stabilization with magnitude limitations. For this problem, we develop a design method for single-input controllable systems with eigenvalues in the left closed plane
Bright vector solitons in cross-defocusing nonlinear media
We study two-dimensional soliton-soliton vector pairs in media with
self-focusing nonlinearities and defocing cross-interactions. The general
properties of the stationary states and their stability are investigated. The
different scenarios of instability are observed using numerical simulations.
The quasi-stable propagation regime of the high-power vector solitons is
revealed.Comment: 6 pages, 7 figure
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