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

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

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

High--Dimensional Brain in a High-Dimensional World: Blessing of Dimensionality

High-dimensional data and high-dimensional representations of reality are inherent features of modern Artificial Intelligence systems and applications of machine learning. The well-known phenomenon of the "curse of dimensionality" states: many problems become exponentially difficult in high dimensions. Recently, the other side of the coin, the "blessing of dimensionality", has attracted much attention. It turns out that generic high-dimensional datasets exhibit fairly simple geometric properties. Thus, there is a fundamental tradeoff between complexity and simplicity in high dimensional spaces. Here we present a brief explanatory review of recent ideas, results and hypotheses about the blessing of dimensionality and related simplifying effects relevant to machine learning and neuroscience.Comment: 18 pages, 5 figure

Blessing of dimensionality at the edge

In this paper we present theory and algorithms enabling classes of Artificial Intelligence (AI) systems to continuously and incrementally improve with a-priori quantifiable guarantees - or more specifically remove classification errors - over time. This is distinct from state-of-the-art machine learning, AI, and software approaches. Another feature of this approach is that, in the supervised setting, the computational complexity of training is linear in the number of training samples. At the time of classification, the computational complexity is bounded by few inner product calculations. Moreover, the implementation is shown to be very scalable. This makes it viable for deployment in applications where computational power and memory are limited, such as embedded environments. It enables the possibility for fast on-line optimisation using improved training samples. The approach is based on the concentration of measure effects and stochastic separation theorems and is illustrated with an example on the identification faulty processes in Computer Numerical Control (CNC) milling and with a case study on adaptive removal of false positives in an industrial video surveillance and analytics system

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

Agile gesture recognition for capacitive sensing devices: adapting on-the-job

Automated hand gesture recognition has been a focus of the AI community for decades. Traditionally, work in this domain revolved largely around scenarios assuming the availability of the flow of images of the user hands. This has partly been due to the prevalence of camera-based devices and the wide availability of image data. However, there is growing demand for gesture recognition technology that can be implemented on low-power devices using limited sensor data instead of high-dimensional inputs like hand images. In this work, we demonstrate a hand gesture recognition system and method that uses signals from capacitive sensors embedded into the etee hand controller. The controller generates real-time signals from each of the wearer five fingers. We use a machine learning technique to analyse the time series signals and identify three features that can represent 5 fingers within 500 ms. The analysis is composed of a two stage training strategy, including dimension reduction through principal component analysis and classification with K nearest neighbour. Remarkably, we found that this combination showed a level of performance which was comparable to more advanced methods such as supervised variational autoencoder. The base system can also be equipped with the capability to learn from occasional errors by providing it with an additional adaptive error correction mechanism. The results showed that the error corrector improve the classification performance in the base system without compromising its performance. The system requires no more than 1 ms of computing time per input sample, and is smaller than deep neural networks, demonstrating the feasibility of agile gesture recognition systems based on this technology.Depto. de Análisis Matemático y Matemática AplicadaFac. de Ciencias MatemáticasFALSEunpu

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