89 research outputs found
Adaptive observers for nonlinearly parameterized systems subjected to parametric constraints
We consider the problem of adaptive observer design in the settings when the
system is allowed to be nonlinear in the parameters, and furthermore they are
to satisfy additional feasibility constraints. A solution to the problem is
proposed that is based on the idea of universal observers and non-uniform
small-gain theorem. The procedure is illustrated with an example.Comment: 19th IFAC World Congress on Automatic Control, 10869-10874, South
Africa, Cape Town, 24th-29th August, 201
Approximation with Random Bases: Pro et Contra
In this work we discuss the problem of selecting suitable approximators from
families of parameterized elementary functions that are known to be dense in a
Hilbert space of functions. We consider and analyze published procedures, both
randomized and deterministic, for selecting elements from these families that
have been shown to ensure the rate of convergence in norm of order
, where is the number of elements. We show that both randomized and
deterministic procedures are successful if additional information about the
families of functions to be approximated is provided. In the absence of such
additional information one may observe exponential growth of the number of
terms needed to approximate the function and/or extreme sensitivity of the
outcome of the approximation to parameters. Implications of our analysis for
applications of neural networks in modeling and control are illustrated with
examples.Comment: arXiv admin note: text overlap with arXiv:0905.067
Further Results on Lyapunov-Like Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems
We provide several characterizations of convergence to unstable equilibria in
nonlinear systems. Our current contribution is three-fold. First we present
simple algebraic conditions for establishing local convergence of non-trivial
solutions of nonlinear systems to unstable equilibria. The conditions are based
on the earlier work (A.N. Gorban, I.Yu. Tyukin, E. Steur, and H. Nijmeijer,
SIAM Journal on Control and Optimization, Vol. 51, No. 3, 2013) and can be
viewed as an extension of the Lyapunov's first method in that they apply to
systems in which the corresponding Jacobian has one zero eigenvalue. Second, we
show that for a relevant subclass of systems, persistency of excitation of a
function of time in the right-hand side of the equations governing dynamics of
the system ensure existence of an attractor basin such that solutions passing
through this basin in forward time converge to the origin exponentially.
Finally we demonstrate that conditions developed in (A.N. Gorban, I.Yu. Tyukin,
E. Steur, and H. Nijmeijer, SIAM Journal on Control and Optimization, Vol. 51,
No. 3, 2013) may be remarkably tight.Comment: 53d IEEE Conference on Decision and Control, Los-Angeles, USA, 201
Lyapunov-like Conditions of Forward Invariance and Boundedness for a Class of Unstable Systems
We provide Lyapunov-like characterizations of boundedness and convergence of
non-trivial solutions for a class of systems with unstable invariant sets.
Examples of systems to which the results may apply include interconnections of
stable subsystems with one-dimensional unstable dynamics or critically stable
dynamics. Systems of this type arise in problems of nonlinear output
regulation, parameter estimation and adaptive control.
In addition to providing boundedness and convergence criteria the results
allow to derive domains of initial conditions corresponding to solutions
leaving a given neighborhood of the origin at least once. In contrast to other
works addressing convergence issues in unstable systems, our results require
neither input-output characterizations for the stable part nor estimates of
convergence rates. The results are illustrated with examples, including the
analysis of phase synchronization of neural oscillators with heterogenous
coupling
Observers for canonic models of neural oscillators
We consider the problem of state and parameter estimation for a wide class of
nonlinear oscillators. Observable variables are limited to a few components of
state vector and an input signal. The problem of state and parameter
reconstruction is viewed within the classical framework of observer design.
This framework offers computationally-efficient solutions to the problem of
state and parameter reconstruction of a system of nonlinear differential
equations, provided that these equations are in the so-called adaptive observer
canonic form. We show that despite typical neural oscillators being locally
observable they are not in the adaptive canonic observer form. Furthermore, we
show that no parameter-independent diffeomorphism exists such that the original
equations of these models can be transformed into the adaptive canonic observer
form. We demonstrate, however, that for the class of Hindmarsh-Rose and
FitzHugh-Nagumo models, parameter-dependent coordinate transformations can be
used to render these systems into the adaptive observer canonical form. This
allows reconstruction, at least partially and up to a (bi)linear
transformation, of unknown state and parameter values with exponential rate of
convergence. In order to avoid the problem of only partial reconstruction and
to deal with more general nonlinear models in which the unknown parameters
enter the system nonlinearly, we present a new method for state and parameter
reconstruction for these systems. The method combines advantages of standard
Lyapunov-based design with more flexible design and analysis techniques based
on the non-uniform small-gain theorems. Effectiveness of the method is
illustrated with simple numerical examples
Simple model of complex dynamics of activity patterns in developing networks of neuronal cultures
Living neuronal networks in dissociated neuronal cultures are widely known
for their ability to generate highly robust spatiotemporal activity patterns in
various experimental conditions. These include neuronal avalanches satisfying
the power scaling law and thereby exemplifying self-organized criticality in
living systems. A crucial question is how these patterns can be explained and
modeled in a way that is biologically meaningful, mathematically tractable and
yet broad enough to account for neuronal heterogeneity and complexity. Here we
propose a simple model which may offer an answer to this question. Our
derivations are based on just few phenomenological observations concerning
input-output behavior of an isolated neuron. A distinctive feature of the model
is that at the simplest level of description it comprises of only two
variables, a network activity variable and an exogenous variable corresponding
to energy needed to sustain the activity and modulate the efficacy of signal
transmission. Strikingly, this simple model is already capable of explaining
emergence of network spikes and bursts in developing neuronal cultures. The
model behavior and predictions are supported by empirical observations and
published experimental evidence on cultured neurons behavior exposed to oxygen
and energy deprivation. At the larger, network scale, introduction of the
energy-dependent regulatory mechanism enables the network to balance on the
edge of the network percolation transition. Network activity in this state
shows population bursts satisfying the scaling avalanche conditions. This
network state is self-sustainable and represents a balance between global
network-wide processes and spontaneous activity of individual elements
Linear stability analysis of the flow between rotating cylinders of wide gap
© 2018 The Authors. Published by Elsevier. This is an open access article available under a Creative Commons licence.
The published version can be accessed at the following link on the publisher’s website: https://doi.org/10.1016/j.euromechflu.2018.07.002© 2018 The Authors This study investigated by an analytical method the flow that develops in the gap between concentric rotating cylinders when the Taylor number Ta exceeds the first critical value. Concentric cylinders rotating at the speed ratio μ=0 are investigated over the radius ratio range 0.20≤η≤0.95. This range includes configurations characterised by a larger annular gap width d than classical journal bearing test cases and by a Taylor number beyond the first critical Taylor number at which Taylor vortices develop. The analysis focuses on determining the parameters for the direct transition from axisymmetric Couette flow to wavy Taylor vortex flow. The results show a marked change in trend as the radius ratio η reduces below 0.49 and 0.63 for the azimuthal wave-numbers m=2 and 3 respectively. The axial wavenumber increases so that the resulting wavy Taylor vortex flow is characterised by vortex structures elongated in the radial direction, with a meridional cross-section that is significantly elliptical. The linear stability analysis of the perturbation equations suggests this instability pattern is neutrally stable. Whereas a direct transition from axisymmetric Couette flow is not necessarily the only route for the onset of wavy Taylor vortex flow, the significant difference between the predicted pattern at large gap widths and classical wavy Taylor vortex flow merits further investigation.This project has been supported by a Specific Targeted Research Project of the European Community’s Sixth Framework Programme under contract number NMP3-CT-2006-032669 (PROVAEN). The original acquisition of MATLAB software licenses was part-funded by EPSRC grant GR/N23745/01.Published versio
MuPix7 - A fast monolithic HV-CMOS pixel chip for Mu3e
The MuPix7 chip is a monolithic HV-CMOS pixel chip, thinned down to 50 \mu m.
It provides continuous self-triggered, non-shuttered readout at rates up to 30
Mhits/chip of 3x3 mm^2 active area and a pixel size of 103x80 \mu m^2. The hit
efficiency depends on the chosen working point. Settings with a power
consumption of 300 mW/cm^2 allow for a hit efficiency >99.5%. A time resolution
of 14.2 ns (Gaussian sigma) is achieved. Latest results from 2016 test beam
campaigns are shown.Comment: Proceedingsfor the PIXEL2016 conference, submitted to JINST A
dangling reference has been removed from this version, no other change
Dynamic Algorithms of Multilayered Neural Networks Training in Generalized Training Plant
The new modifications of multilayered neurak networks training algorithms in a generalized training plant structure are introduced. The first modification for algorithm "on error backpropagation algorithm through time" is introduced and its sufficient conditions of a training procedure stability are obtained. Other modification for speed gradient algorithm of an error backpropagation is obtained, where measurement state vector in a training procedure instead of a parametrical model of plant is used
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