6,044 research outputs found
Modulational instability in dispersion oscillating fiber ring cavities
We show that the use of a dispersion oscillating fiber in passive cavities
significantly extend modulational instability to novel high-frequency bands,
which also destabilize the branches of the steady response which are stable
with homogeneous dispersion. By means of Floquet theory, we obtain exact
explicit expression for the sideband gain, and a simple analytical estimate for
the frequencies of maximum gain. Numerical simulations show that stable
stationary trains of pulses can be excited in the cavity
Integral MRAC with Minimal Controller Synthesis and bounded adaptive gains: The continuous-time case
Model reference adaptive controllers designed via the Minimal Control Synthesis (MCS) approach are a viable solution to control plants affected by parameter uncertainty, unmodelled dynamics, and disturbances. Despite its effectiveness to impose the required reference dynamics, an apparent drift of the adaptive gains, which can eventually lead to closed-loop instability or alter tracking performance, may occasionally be induced by external disturbances. This problem has been recently addressed for this class of adaptive algorithms in the discrete-time case and for square-integrable perturbations by using a parameter projection strategy [1]. In this paper we tackle systematically this issue for MCS continuous-time adaptive systems with integral action by enhancing the adaptive mechanism not only with a parameter projection method, but also embedding a s-modification strategy. The former is used to preserve convergence to zero of the tracking error when the disturbance is bounded and L2, while the latter guarantees global uniform ultimate boundedness under continuous L8 disturbances. In both cases, the proposed control schemes ensure boundedness of all the closed-loop signals. The strategies are numerically validated by considering systems subject to different kinds of disturbances. In addition, an electrical power circuit is used to show the applicability of the algorithms to engineering problems requiring a precise tracking of a reference profile over a long time range despite disturbances, unmodelled dynamics, and parameter uncertainty.Postprint (author's final draft
A characterization of switched linear control systems with finite L 2 -gain
Motivated by an open problem posed by J.P. Hespanha, we extend the notion of
Barabanov norm and extremal trajectory to classes of switching signals that are
not closed under concatenation. We use these tools to prove that the finiteness
of the L2-gain is equivalent, for a large set of switched linear control
systems, to the condition that the generalized spectral radius associated with
any minimal realization of the original switched system is smaller than one
Uphill Motion of Active Brownian Particles in Piecewise Linear Potentials
We consider Brownian particles with the ability to take up energy from the
environment, to store it in an internal depot, and to convert internal energy
into kinetic energy of motion. Provided a supercritical supply of energy, these
particles are able to move in a ``high velocity'' or active mode, which allows
them to move also against the gradient of an external potential. We investigate
the critical energetic conditions of this self-driven motion for the case of a
linear potential and a ratchet potential. In the latter case, we are able to
find two different critical conversion rates for the internal energy, which
describe the onset of a directed net current into the two different directions.
The results of computer simulations are confirmed by analytical expressions for
the critical parameters and the average velocity of the net current. Further,
we investigate the influence of the asymmetry of the ratchet potential on the
net current and estimate a critical value for the asymmetry in order to obtain
a positive or negative net current.Comment: accepted for publication in European Journal of Physics B (1999), for
related work see http://summa.physik.hu-berlin.de/~frank/active.htm
Spatially structured oscillations in a two-dimensional excitatory neuronal network with synaptic depression
We study the spatiotemporal dynamics of a two-dimensional excitatory neuronal network with synaptic depression. Coupling between populations of neurons is taken to be nonlocal, while depression is taken to be local and presynaptic. We show that the network supports a wide range of spatially structured oscillations, which are suggestive of phenomena seen in cortical slice experiments and in vivo. The particular form of the oscillations depends on initial conditions and the level of background noise. Given an initial, spatially localized stimulus, activity evolves to a spatially localized oscillating core that periodically emits target waves. Low levels of noise can spontaneously generate several pockets of oscillatory activity that interact via their target patterns. Periodic activity in space can also organize into spiral waves, provided that there is some source of rotational symmetry breaking due to external stimuli or noise. In the high gain limit, no oscillatory behavior exists, but a transient stimulus can lead to a single, outward propagating target wave
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